What does a car’s speedometer measure?
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Instantaneous speed.
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What does a car’s speedometer measure?
Instantaneous speed.
Which quantity is the highway patrol more interested in for prosecution?
Average speed.
What does a steeper slope indicate in terms of instantaneous velocity?
A greater instantaneous velocity.
What does the direction of the acceleration vector indicate?
It indicates the direction of the change in velocity (∆v).
What can the highway patrol be 100% certain of if your average speed exceeds the posted limit?
Your instantaneous speed was over the posted limit.
What does a steep slope on a graph indicate?
A rapid change in velocity (or speed) and thus a large acceleration.
What is the formula for calculating average acceleration?
a = Δv / Δt.
What is the total distance of the trip from Kingman to Phoenix?
260 miles.
What is the runner's goal in the 100-m Dash?
To reach top speed as soon as possible.
What does the vertical axis represent in the graph?
Distance.
What is the significance of slope in a velocity-time graph?
It represents acceleration.
What do our bodies feel instead of constant velocity?
Acceleration.
What does a decreasing slope on the velocity curve indicate?
It indicates that the acceleration is decreasing.
What is instantaneous speed?
The speed at which an object is moving at a specific instant in time.
How is the magnitude of instantaneous velocity related to instantaneous speed?
The magnitude is equal to the instantaneous speed at that moment.
In a graph representing acceleration versus time, what does the horizontal axis represent?
Time.
At which point is the magnitude of the acceleration the greatest?
At the point where the velocity is changing the fastest.
Is the distance traveled the same for all time intervals?
No, it varies based on the area under the velocity curve.
What happens to the car's velocity between 4 s and 6 s?
The velocity is decreasing but still positive.
Is the velocity constant between 0 s and 2 s?
Yes, the velocity is constant during this interval as the graph is flat with a slope of zero.
What does the speedometer measure?
The instantaneous speed at a given moment.
What does the acceleration graph for uniform acceleration look like?
A horizontal line.
What is the average speed from Kingman to Flagstaff?
50.0 mph.
What does the direction of the acceleration vector indicate?
It indicates the direction of the change in velocity (∆v).
What happens to velocity between 2 s and 4 s?
The velocity is changing fastest.
Why doesn't a speedometer measure velocity?
Because it does not account for direction.
What happens to acceleration when speed is constant but the direction of velocity changes?
The acceleration is at right angles to the velocity.
Can you give an example of uniform acceleration?
A car moving along a straight road and accelerating at a constant rate.
What does a horizontal line on a graph represent?
Zero slope, indicating zero acceleration.
When does the velocity change in relation to the distance graph?
The velocity changes only when the slope of the distance graph changes.
What is the average speed from Kingman to Flagstaff?
50.0 mph.
When does uniform acceleration occur?
Whenever there is a constant force acting on an object.
How does the distance covered change over time in uniform acceleration?
It grows more and more rapidly with time.
What is instantaneous acceleration?
The acceleration at a precise instant in time.
What happens during the remaining portion of the 100-m Dash after reaching top speed?
The runner continues at a constant speed, so acceleration is zero.
How is average acceleration calculated?
(Final velocity - Initial velocity) ÷ (Time interval).
What are the units of acceleration?
Units of velocity divided by units of time.
What are the coordinates of the second data point?
5 seconds and 4.1 cm.
When is the car not moving at all?
When the graph is flat (slope is zero).
What is instantaneous velocity?
A vector quantity that represents the velocity at a specific instant in time.
What does the direction of the acceleration vector indicate?
It indicates the direction of the change in velocity (∆v).
What does the speed limit indicate?
The maximum legal instantaneous speed.
When is the velocity considered constant in a distance vs. time graph?
When the slope of the distance vs. time graph is constant.
What does the horizontal axis represent in the graph?
Time.
Is the acceleration of the object constant based on the velocity graph?
No, the acceleration is decreasing.
What is the final velocity of the car after 5 seconds?
20 m/s due east.
How does a graph compare to a simple table in displaying information?
A graph displays information in a more useful manner than a simple table.
What is a common example of uniform acceleration?
A falling rock or other falling object.
What is the initial velocity of the car in this example?
Zero.
How is instantaneous acceleration defined?
As the rate at which velocity is changing at a given instant in time.
What are the two components of velocity?
Magnitude (speed) and direction.
How can instantaneous acceleration be calculated?
By calculating the average speed over a short enough time that the speed does not change much.
What is the distance from Kingman to Flagstaff?
120 miles.
What is the distance from Flagstaff to Phoenix?
140 miles.
How often should we note the car's position to describe its motion?
Every 5 seconds.
What are some units of speed?
Miles per hour, meters per second, kilometers per hour, inches per minute.
What two components define instantaneous velocity?
Magnitude (instantaneous speed) and direction of motion.
What does the direction of instantaneous velocity indicate?
The direction of motion at that specific instant.
During which time interval is the acceleration greatest?
Between 2 s and 4 s.
Does the car ever go backward according to the motion described?
No, never.
What is uniform acceleration?
The simplest form of acceleration where a constant force acts on an object.
What does the distance graph for uniform acceleration show?
A constantly increasing slope due to constantly increasing velocity.
What is the definition of rate?
One quantity divided by another quantity.
What type of quantity is velocity?
Velocity is a vector quantity.
How is average acceleration calculated in this scenario?
By dividing the change in velocity (12 m/s) by the time interval (8 seconds).
When is the magnitude of acceleration greatest?
When the velocity is changing the fastest.
What are the possible answers for the average acceleration?
a) 4 m/s², b) 3 m/s², c) 2 m/s², d) 1.5 m/s², e) 1 m/s².
How is average speed defined?
The rate at which distance is covered over time.
How does the velocity change over time in uniform acceleration?
It increases at a steady rate.
What is the formula used to calculate average acceleration in this scenario?
4 m/s ÷ 4 sec = 1 m/s².
What is the formula for acceleration in terms of change in velocity and time?
a = Δv / t.
How is distance (d) calculated when starting from rest?
d = vt = 1/2 at².
How can instantaneous velocities at two points be compared?
By looking at their slopes on a graph.
What happens to the acceleration when velocity is increasing?
The acceleration is in the same direction as the velocity.
What is the average speed from Flagstaff to Phoenix?
53.8 mph.
What is acceleration?
The rate at which velocity changes.
What does acceleration refer to?
Any change in velocity.
Why is the average of the average accelerations from 0 to 4 sec and 4 to 8 sec the same as from 0 to 8 sec?
Because the total change in velocity over the entire time period is the sum of the changes in each segment.
What does the slope of the velocity graph represent?
The acceleration.
What does each interval on an axis represent?
A fixed quantity of distance or time.
How is the distance at any instant calculated?
Distance is velocity times the time at that instant.
How is slope calculated on a graph?
Change in vertical quantity divided by change in horizontal quantity.
What is the position of the car at 0 seconds?
0.0 cm.
At position B, how does the velocity vector v2 compare to v1?
It has the same magnitude but a different direction.
What can a change in velocity indicate?
A change in the object's speed or direction of motion.
What does a speedometer indicate?
Instantaneous speed, but not velocity.
What is the car's position at 25 seconds?
16.0 cm.
What is the main idea expressed about acceleration?
It's not the fall that hurts, but the sudden stop at the end.
What happens to acceleration over time in uniform acceleration?
It does not change.
What type of quantity is acceleration?
Acceleration is a vector quantity, with magnitude and direction.
What indicates the greatest magnitude of acceleration on a velocity vs. time graph?
The steepest slope of the graph.
What does the velocity graph for uniform acceleration look like?
A straight line with a constant slope.
What is the total time taken for the trip from Kingman to Phoenix?
5.0 hours.
Can a decrease in velocity be considered acceleration?
Yes, a decrease in velocity (slowing down) is also referred to as acceleration.
What is the initial velocity of the car?
0 m/s (starting from rest).
Give an example of acceleration in everyday life.
A car changing speed or direction.
How does a car demonstrate uniform acceleration?
By accelerating at a constant rate.
Why is the average speed for the whole trip not the average of the two speeds?
Because the distances and times are different, affecting the overall average.
How many seconds are in one hour?
3600 seconds (60 minutes x 60 seconds).
What is the time interval for calculating average acceleration in this scenario?
4 seconds (from 4 s to 8 s).
What is the first step in converting 70 km/h to m/s?
Convert kilometers to meters by multiplying by 1000.
What happens to the acceleration when velocity is decreasing?
The acceleration is in the opposite direction to the velocity.
During which time interval is the distance traveled by the car the greatest?
Between 2 s and 4 s.
What indicates the greatest distance traveled in a velocity-time graph?
The area under the velocity curve.
Does a car's velocity change when it goes around a curve at constant speed?
Yes.
What is being compared in terms of average acceleration?
The average accelerations from 0 to 4 seconds, 4 to 8 seconds, and 0 to 8 seconds.
What do our bodies feel when velocity is constant?
Our bodies don’t feel velocity.
What does it mean when the acceleration does not change?
The acceleration remains constant throughout the motion.
What is the average speed from Flagstaff to Phoenix?
53.8 mph.
What is an example of a rate?
Gallons per minute, pesos per dollar, points per game.
When is the car moving the fastest according to the graph?
The specific time can be determined by analyzing the steepest slope on the graph.
What are the coordinates of the first data point?
0 seconds and 0 cm.
How is the total distance covered calculated in uniform acceleration?
Total distance is average velocity times the total elapsed time.
What does 'rise over run' refer to?
It is a way to describe the calculation of slope.
What can acceleration involve?
A change in the object's speed or direction of motion.
What does a flat slope indicate on the graph?
A slope of zero between 20 s and 30 s.
What is the car's position at 35 seconds?
18.0 cm.
What does the direction of the acceleration vector indicate?
It indicates the direction of the change in velocity (∆v).
What do the horizontal and vertical axes represent in the car's velocity graph?
The horizontal axis represents time, and the vertical axis represents velocity.
In a graph representing acceleration versus time, what does the vertical axis represent?
Acceleration.
What type of road is mentioned in the example?
A local highway.
What is the average acceleration of the car between 0 s and 8 s?
1.5 m/s².
What happens to the velocity of the object over time according to the graph?
The velocity initially changes rapidly, reaches a maximum value, and then remains constant.
What does the slope at any point on a distance-versus-time graph represent?
The instantaneous velocity at that time.
What are the units of velocity?
Units of distance divided by units of time.
At position A, what is indicated by the velocity vector v1?
The velocity of the car at that position.
What does the distance traveled represent in relation to a velocity graph?
The area under the velocity graph.
What are the initial and final velocities used in the average acceleration calculation?
Initial velocity is 4 m/s and final velocity is 12 m/s.
How can the units of acceleration be expressed?
As units of (distance divided by time) divided by units of time.
What is the relationship between final velocity and acceleration?
Final velocity (v) is equal to at.
What is the final calculation to convert 70,000 m/h to m/s?
70,000 m/h divided by 3600 gives 19.4 m/s.
What does the slope of a velocity graph represent?
Acceleration.
What happens to the velocity of a car over time in this scenario?
The velocity of the car increases with time.
Does the car ever go backward according to the graph?
Yes, during the third segment (not labeled).
What is the average acceleration of the car?
4 m/s².
What indicates that the car is moving backward?
The distance traveled is decreasing during the third segment.
When does the greatest acceleration occur in the 100-m Dash?
At the beginning of the race.
What does a flat graph indicate about velocity?
It indicates that the velocity is constant and not changing.
What does the area of the rectangle represent in the distance formula?
The distance the object would travel with constant velocity v0 for a time t.
What is the average speed for the whole trip?
52.0 mph.
How is average acceleration calculated?
By dividing the change in velocity by the time taken.
Can we determine the acceleration from the velocity graph?
It is impossible to determine from this graph.
What is the formula for total distance covered with initial velocity and acceleration?
d = v0 t + 1/2 at².
What is 70 kilometers per hour in meters per second?
19.4 m/s.
What does a negative slope indicate on the graph?
A decrease in distance between 50 s and 60 s.
What is the conclusion about the instantaneous velocity at point A compared to point B?
The velocity at A is greater than at B.
What indicates the greatest acceleration on a graph?
The steepest slope.
What is the formula for average acceleration?
a = Δv / t, where Δv is the change in velocity and t is the elapsed time.
What does velocity involve?
Direction of motion and how fast the object is going.
What does the total distance covered consist of for a non-zero initial velocity?
The area of the triangle plus the rectangle.
What is the average acceleration of the car between 4 s and 8 s?
2 m/s².
What is the overall average speed for the trip from Kingman to Phoenix?
52.0 mph.
What is the slope of the graph between 0 s and 2 s?
The slope is zero.
What is the conversion factor from kilometers to meters?
1 km = 1000 m.
What role does friction play when a car rounds a curve?
Friction between the wheels and the road exerts a force to change the car’s direction.
What is the formula for average velocity when starting from zero initial velocity?
Average velocity is 1/2 (at).
How is instantaneous speed calculated?
By calculating the average speed over a short enough time that the speed does not change much.
What is the car's position at 15 seconds?
12.1 cm.
What remains constant while a car goes around a curve?
The speed of the car.
How is average acceleration defined?
As the change in velocity divided by the time required to produce that change.
What changes as the car moves from position A to position B?
The direction of the velocity vector.
What is the average acceleration of the car between 0 s and 4 s?
1 m/s².
What is the significance of velocity being positive?
It indicates the car is moving in the same direction and not backward.
How long does the car take to reach 20 m/s?
5 seconds.
What is instantaneous speed?
The speed at that precise instant in time.
How does a wall affect a bouncing ball?
The wall exerts a force on the ball, causing it to change direction.
What two aspects of velocity can be changed by a force?
The magnitude (speed) or direction.
How do you convert kilometers per hour to meters per second?
Multiply by 1000 to convert kilometers to meters, then divide by 3600 (60 minutes x 60 seconds) to convert hours to seconds.
What is speed?
Speed is how fast an object changes its location.
Is it easier to multiply by 0.6214 or divide by 1.609 for conversion?
It is easier to multiply by 0.6214.
Is the car moving backward between 4 s and 6 s?
No, it is not moving backward as the velocity remains positive.
In which segment is the car confirmed to be moving backward?
In the third segment (not labeled).
What do vectors have?
Both magnitude and direction.
What is required to produce a change in velocity?
A force.
What does the area of the triangle represent in the distance formula?
The additional distance traveled due to acceleration.
How does an elevator demonstrate acceleration?
By speeding up or slowing down.
What is the car's position at 5 seconds?
4.1 cm.
What is the car's position at 10 seconds?
7.9 cm.
What is the car's position at 20 seconds?
16.0 cm.
What does a decreasing distance on a position-time graph signify?
The car is moving backward (in reverse).
When is the car moving the slowest?
When the slope of the graph is the least steep.
What happens to acceleration during uniform acceleration?
The acceleration does not change as the motion proceeds.
When is the slope steepest on the graph?
Between 0 s and 20 s.
What is the formula to calculate final velocity in uniform acceleration?
v = v₀ + at.
At what time does the car start moving in the opposite direction?
When the graph crosses the axis indicating a change in direction.
What is the car's position at 30 seconds?
16.0 cm.
How is speed calculated?
Speed is always some distance divided by some time.
How is average speed defined?
Average speed is total distance divided by total time.
What is the formula for average speed?
Average speed = distance traveled / time of travel.
How do you convert kilometers per hour to miles per hour?
Multiply by 0.6214.
What is the conversion factor from kilometers to miles?
1 km = 0.6214 miles.
What is the result of converting 70 kilometers per hour to miles per hour?
43.5 miles per hour (MPH).
