1. Describing Motion in One Dimension
Acceleration and Motion Graphs

2. Acceleration Acceleration is a measure of how quickly velocity changes
It is the rate of change of velocity
Acceleration describes how velocity is changing over time, it is also a vector quantity whose direction is that of the velocity change.

3. Acceleration
The velocity of the car is increasing by 10 km h-1 each second, therefore the acceleration of the car is +10 km per hour per second
The velocity of the athlete is decreasing by 2 m s-1 therefore it’s acceleration is – 2 m s-2

4. Acceleration Average acceleration is the rate of change of velocity
Where v is the final velocity (m s-1)
u is the initial velocity (m s-1)
Δt is the time interval (s)
Acceleration is measured in metres per second squared (m s-2)

5. Acceleration Example
A cheetah running at 20 m s-1 slows down as it approaches a stream. Within 3.0 s, its speed has reduced to 2 m s-1. Calculate the average acceleration of the cheetah.

6. Graphing motion: position, velocity and acceleration
At time, even the motion of an object travelling in a straight line can be complicated.
The object may travel forwards or backwards, speed up or slow down, or even stop.
This information can be presented in graphical form.
The advantage of presenting information in graph is that it allows the nature of the motion to be seen clearly.

7. Graphing position
A position-time graph indicates the position of an object at any time for motion that occurs over an extended time interval.

8. s = final position – initial position
The displacement of the object in motion can be determined by comparing initial and final positions
s = final position – initial position
e.g between 20s and 60s
s = 25 – 40 = -15m
(the negative sign in front represents the direction of displacement)
The velocity is given by the gradient (slope) of a position-time graph.
A positive velocity indicates that the object is moving in a positive direction, and a negative velocity indicates motion in a negative direction.

9. A car driven by a learner driver travels along a straight driveway and is initially heading north. The position of the car is shown in the graph.
a. Describe the motion of the car in terms of its position.
b. What is the displacement of the car during the first 10s of its motion?
c. What distance has the car travelled during the first 10s?
d. Calculate the average velocity of the car during the first 4s.
e. Calculate the average velocity of the car between t = 6s and t = 20s.
f. Calculate the average velocity of the car during its 20s trip.
g. Calculate the average speed of the car during its 20s trip.

10. A car driven by a learner driver travels along a straight driveway and is initially heading north. The position of the car is shown in the graph.
Describe the motion of the car in terms of its position.
b. What is the displacement of the car during the first 10s of its motion?

11. A car driven by a learner driver travels along a straight driveway and is initially heading north. The position of the car is shown in the graph.
c. What distance has the car travelled during the first 10s?
d. Calculate the average velocity of the car during the first 4s.

12. A car driven by a learner driver travels along a straight driveway and is initially heading north. The position of the car is shown in the graph.
e. Calculate the average velocity of the car between t = 6s and t = 20s.
f. Calculate the average velocity of the car during its 20s trip.

13. A car driven by a learner driver travels along a straight driveway and is initially heading north. The position of the car is shown in the graph.
g. Calculate the average speed of the car during its 20s trip.

14. Graphing velocity
A graph of velocity against time shows how the velocity changes with time
For example if we have a girl running up and down an aisle in a supermarket.
In the velocity time graph we see that her velocity for the first 4 seconds is constant at 3 m s-1 in the positive direction. Between 4 and 6 s her direction is still the same, positive, but she begins to slow down. She then comes to a stop for 1 s, before changing direction in the final 3 seconds, when her velocity is negative.

15. Graphing velocity
A velocity time graph can also be used to find the displacement of the body under consideration.
Displacement is given by the area under a velocity-time graph (or the area between the line and the time axis).
It is important to note that an area below the time axis indicates a negative displacement, i.e motion in a negative direction.

16. Graphing velocity
A velocity time graph can also be used to find the acceleration of the body under consideration.
Average acceleration is the gradient of a velocity-time graph of the object over the time interval.
If the acceleration is changing, the velocity-time graph will be curved, the velocity-time graph will be curved, and so the gradient of the tangent will give an instantaneous acceleration.

17. The motion of a radio controlled car travelling in a straight line across a driveway is represented by the graph below.
Describe the motion of the car in terms of its velocity.
Calculate the displacement of the car during the first 4 s.
Calculate the average velocity of the car during the first 4 s
Determine the displacement for the 9 s shown.
Find the acceleration during the first 4s
Find the acceleration from 4 s to 6 s.

18. The motion of a radio controlled car travelling in a straight line across a driveway is represented by the graph below.
a. Describe the motion of the car in terms of its velocity.
b. Calculate the displacement of the car during the first 4 s.

19. The motion of a radio controlled car travelling in a straight line across a driveway is represented by the graph below.
c. Calculate the average velocity of the car during the first 4 s.

20. The motion of a radio controlled car travelling in a straight line across a driveway is represented by the graph below.
d. Determine the displacement for the 9 s shown.
e. Find the acceleration during the first 4 s.

21. The motion of a radio controlled car travelling in a straight line across a driveway is represented by the graph below.
f. Find the acceleration from 4 s to 6 s.