Question

The figure below shows a velocity-time graph of a train between two stations.
Find the acceleration of the train in each of the time intervals OX, XY, and YZ respectively.

• A. $-2m{s}^{-2},1m{s}^{-2},4m{s}^{-2}$
• B. $2m{s}^{-2},1m{s}^{-2},-4m{s}^{-2}$
• C. $-2m{s}^{-2},0m{s}^{-2},4m{s}^{-2}$
• D. $2m{s}^{-2},0m{s}^{-2},-4m{s}^{-2}$

Answer 1

The correct option is D $2m{s}^{-2},0m{s}^{-2},-4m{s}^{-2}$

Since the velocity-time graph is a straight line in the given intervals, we can conclude that the acceleration is constant in each of these intervals.
We know: $\text{Acceleration}=\frac{\text{Final velocity}-\text{Initial velocity}}{\text{Time taken}}$

$\therefore$ In the interval OX, acceleration $=\frac{12-0}{6-0}=2m{s}^{-2}$

In the interval XY, acceleration $=\frac{12-12}{18-6}=0m{s}^{-2}$

In the interval YZ, acceleration $=\frac{0-12}{21-18}=-4m{s}^{-2}$