# Question Video: The Velocity–Time Graph Mathematics

Given the velocity–time graph for a particle that moved in a straight line, determine its acceleration at 𝑡 = 3 s.

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### Video Transcript

Given the velocity–time graph for a particle that moved in a straight line, determine its acceleration at 𝑡 equals three seconds.

As our graph is linear, we know that the acceleration is constant. We can calculate the acceleration by dividing the change in velocity by the change in time. This will calculate the gradient of our straight line. By drawing a right-angled triangle, we can see that the velocity changed from zero centimeters per second to 210 centimeters per second.

This took a total of 10 seconds, from zero to 10. The acceleration is therefore equal to 210 divided by 10. This equals 21. And our units are centimeters per second per second or centimeters per second squared. The acceleration for the whole journey including when 𝑡 equals three seconds is 21 centimeters per second squared.