Question

(a) Explain how you can determine the acceleration over time from a velocity versus time graph such as the one in Figure 2.56.

(b) Based on the graph, how does acceleration change over time?

Short answer

a) The slope of a velocity vs. time graph gives the value of instantaneous acceleration.

b) the acceleration increases slowly from point P to Q.

Step-by-step solution

Determination of acceleration

The acceleration of a body is calculated by the change in the velocity of the body with respect to that of time.

Here in the graph, at point P, the velocity of the object is V₁, and the time taken to reach that velocity is T₁.

If we take point Q in the graph, then the velocity at that point is V_2, and the time is T₂.

We can clearly see that the velocity is increasing from V₁ to V₂.

Hence it can be said that the acceleration of the body, that is, the change in the value of velocity, will also be positive.

If we want to calculate the acceleration with respect to the graph, we need to calculate the slope at points P and Q.

Slope of velocity versus time graph  

(a) The slope of a velocity vs. time graph gives the value of instantaneous acceleration.

b) Hence from the graph, we can see that slope of the P point is more than the slope at Q.

Here slop means the angle made by the tangent line passing through P and the x-axis.

Hence, we can say that acceleration increases.

By seeing the graph, it is clear that the acceleration increases slowly as we go from point P to Q.