2.10 Gradient of a Speed-Time Graph

2.10 Gradient of a Speed-Time Graph

Now consider the speed-time graph. The speeds at times t₁ and t₂ are v₁ and v₂ respectively. The change in speed in a time interval (t₂ − t₁) is (v₂ − v₁). Therefore:

Slope = Change in speed / Total time taken
Slope = (v₂ − v₁) / (t₂ − t₁)
Slope = Δv / t

But Δv / t = a, the average acceleration.

Hence:

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Gradient of the speed-time graph is equal to the average acceleration of the body.

This shows that when a car moves with constant acceleration, the velocity-time graph is a straight line which rises through the same height for equal intervals of time.

When the speed of the object is constant, the speed-time graph is a horizontal straight line parallel to the time axis. In this case:

v₂ − v₁ = 0
Slope = (v₂ − v₁) / (t₂ − t₁) = 0

This shows that the acceleration of this motion is zero. It is motion without change in speed.