Position vs Time Graph

Imagine you are driving a car and want to merge onto the freeway. Traffic is moving fast, and you only have a few seconds to speed up to the pace of the other cars.  You step on the gas, but your car is old and doesn't have much power.  You know your car can get up to the freeway speed (60 miles per hour), but how long will it take?  

What you need to know is your car's maximum acceleration.  How long does it take to go from a stop (0 mph) to 60 mph?  A Ferrari can do that in 2.4 seconds. A Toyota Camry takes longer, 7.6 seconds, to accelerate from 0 to 60 mph.  

Speed is measured by units of distance/time, for example miles per hour (mph) or meters per second (m/s).  Acceleration is the increase (or decrease) in speed per second. The most common unit used for acceleration  is meters per second per second, or the change in speed (m/s) per second.

What does it feel like when you are accelerated quickly in a car? On a roller coaster? If you are trying to get up to freeway speed quickly, your car will need to increase its acceleration.  To do that you would have to step on the gas.

The graph below shows the position a ball has travelled (in meters) as it rolls down a long ramp.  The position is shown versus time in seconds.  We will use this simple example to start exploring acceleration.

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How many meters had the ball travelled after 2 seconds?

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How many meters had the ball travelled after 4 seconds?

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Compare the time periods 0-2 seconds and 2-4 seconds.
Which statement is true?

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Look at the slope, or steepness of the curve on the graph.
What happens to the curve as time passes?

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Which statement best describes the ball's speed as it travells down the ramp?

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The graph below shows the distance a biker travels over time.

Match three sections of the graph above with the description of the biker's motion during that time period.

Draggable item		Corresponding Item
travelling at a constant speed		A
speeding up		B
stopped		C

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Match the description of the position-time graph with the correct description of the motion.

Draggable item		Corresponding Item
E		constant positive velocity
G		slow, rightward constant velocity
A		slow, leftward constant velocity
B		negative increasing velocity
F		positive increasing velocity
D		fast, rightward constant velocity
C		fast, leftward constant velocity
H		leftward decreasing velocity

Position vs Time Graph

How many meters had the ball travelled after 2 seconds?

How many meters had the ball travelled after 4 seconds?

Compare the time periods 0-2 seconds and 2-4 seconds. Which statement is true?

Look at the slope, or steepness of the curve on the graph. What happens to the curve as time passes?

Which statement best describes the ball's speed as it travells down the ramp?

The graph below shows the distance a biker travels over time. Match three sections of the graph above with the description of the biker's motion during that time period.

Match the description of the position-time graph with the correct description of the motion.

How many meters had the ball travelled after 2 seconds?

How many meters had the ball travelled after 4 seconds?

Compare the time periods 0-2 seconds and 2-4 seconds. Which statement is true?

Look at the slope, or steepness of the curve on the graph. What happens to the curve as time passes?

Which statement best describes the ball's speed as it travells down the ramp?

The graph below shows the distance a biker travels over time. Match three sections of the graph above with the description of the biker's motion during that time period.

Match the description of the position-time graph with the correct description of the motion.

Compare the time periods 0-2 seconds and 2-4 seconds.
Which statement is true?

Look at the slope, or steepness of the curve on the graph.
What happens to the curve as time passes?

The graph below shows the distance a biker travels over time.

Match three sections of the graph above with the description of the biker's motion during that time period.

Compare the time periods 0-2 seconds and 2-4 seconds.
Which statement is true?

Look at the slope, or steepness of the curve on the graph.
What happens to the curve as time passes?

The graph below shows the distance a biker travels over time.

Match three sections of the graph above with the description of the biker's motion during that time period.