Question

Displacement - time curve of a particle moving along a straight line is shown. Tangents at $A$ and $B$ make angles ${45}^{\circ }$ and ${135}^{\circ }$ with positive x-axis respectively. The average acceleration of the particle during $t=1,t=2$ second is

• A. $-2m/s^2$
• B. $1m/s^2$
• C. $-1m/s^2$
• D. Zero

Answer 1

The correct option is A $-2m/s^2$

The slope at any instant of time in $x-1$ graph gives velocity

initial velocity, $u=\tan 45=1,t=1$

final velocity, $v=\tan 135=-1,t=2$

$a=\frac{v-u}{\Delta t}=\frac{-1-1}{1}=-2m{s}^{-2}$

$a=-2m{s}^{-2}$