Acceleration-Time Graphs

Acceleration-time graphs show the acceleration of an object as it moves in a straight line
They show acceleration (on the vertical axis) against time (on the horizontal axis)
Acceleration-time graphs can go below the horizontal axis

A horizontal line shows that the object is accelerating at a constant rate
If the graph touches the x-axis then the object is moving with constant velocity at that time
If the graph is above the x-axis then the object has positive acceleration and its velocity is increasing which means
- It is speeding up if it is moving forward
- It is slowing down if it is moving backwards
If the graph is below the x-axis then the object has negative acceleration and its velocity is decreasing which means
- It is slowing down if it is moving forward
- It is speeding up if it is moving backwards
The area between graph and the x-axis tells us the change in velocity of the object
- Graph above the x-axis means the velocity of the object is increasing
- Graph below the x-axis means the velocity of the object is decreasing
The total change in velocity of the object from its starting point is the sum of the areas above the x-axis minus the sum of the areas below the x-axis

You can not tell the velocity of the object at a specific time just by looking at an acceleration-time graph
- You can calculate this using the areas between the graph and the x-axis if you know the initial velocity of the object
- If the acceleration-time graph is positive this does not guarantee that the velocity will be positive

2-1-3_we_acceleration-time-graph

(i)

the speed of the car after 2 seconds,

(ii)

the distance travelled between the times

t = 2

and

t = 6

(iii)

the speed of the car after 8 seconds.

Most of the time the acceleration-time graphs you will encounter will comprise of three disjointed horizontal lines, acceleration-time graphs will not have curved or diagonal lines for this course. Though in real life acceleration is likely to vary.

Acceleration-Time Graphs (Edexcel International A Level Maths: Mechanics 1)