Question

Motion of a motorcyclist is shown in the figure. Which of the following shows the displacement-time graph for this motion?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We know, $velocity=\frac{displacement}{time}$

From the figure, it is seen that:
In the time interval $0-1$ seconds, the motorcyclist covers $13.5m$ and velocity $=\frac{13.5}{1}=13.5m{s}^{-1}$

In the time interval $1-2$ seconds, the motorcyclist covers $24-13.5=10.5m$ and
velocity $=\frac{10.5}{1}=10.5m{s}^{-1}$

In the time interval $2-3$ seconds, the motorcyclist covers $31.5-24=7.5m$ and velocity $=\frac{7.5}{1}=7.5m{s}^{-1}$

The displacement of the motorcyclist is unequal in equal intervals of time, therefore it is undergoing a non-uniform motion. Since the velocities are reducing, the body is decelerating. Therefore the slope of the displacement-time graph keeps reducing.