Question

A particle has a rectilinear motion and the figure gives its displacement as a function of time. Which of the following statements are true with respect to the motion?

• A. Between $O$ and $A$ the velocity of the particle is positive and acceleration of the particle is negative.
• B. Between $A$ and $B$ the velocity and acceleration of the particle are positive.
• C. Between $B$ and $C$ the velocity of the particle is negative and acceleration of the particle is positive.
• D. Between $D$ and $E$ the acceleration of the particle is positive.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Between $O$ and $A$ the velocity of the particle is positive and acceleration of the particle is negative.
C Between $B$ and $C$ the velocity of the particle is negative and acceleration of the particle is positive.
D Between $D$ and $E$ the acceleration of the particle is positive.

Between $O$ and $A$ the slope of the tangent is +ve $\Rightarrow$ velocity is +ve, but the value of the slope is decreasing i.e., acceleration is negative.

Between $A$ and $B$ slope is -ve $\Rightarrow$ velocity is -ve.

Between $B$ and $C$ the slope of the tangent is -ve $\Rightarrow$ velocity is -ve, but the value of the slope is increasing i.e., acceleration is +ve.

Between $D$ and $E$ the value of the slope is increasing $\Rightarrow$ acceleration is +ve.