Acceleration-Time Graphs (Edexcel IAL Maths)

Spec point — 3.1

Acceleration-Time Graphs

What is an acceleration-time graph?

• 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

What are the key features of an acceleration-time graph?

• 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

What does an acceleration-time graph NOT show?

• 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

Worked Example A traffic tracks a car on the road for an 8-second period. The acceleration-time graph shows the journey of the car.

Given that the car is travelling with speed 25 m s^-1 when the traffic officer starts tracking the car, find:

(i) the speed of the car after 2 seconds,

Answer:

(ii) the distance travelled between the times $t=2$ and $t=6$,

Answer:

(iii) the speed of the car after 8 seconds.

Answer:

Exam Hint

• 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.