Question

Given below are the equations of motion of four particles A, B, C and D

$x_{A}=6t-3; \, \, x_{B}=4t^{2}-2t+3; \, \, \, x_{C}=3t^{3}-2t^{2}+t-7;$ $x_{D}=7 \, cos 60^{o} - 3 sin ⁡ 30^{o} \, \, $

The particle moving with constant acceleration is

• A. A
• B. B
• C. C
• D. D

Answer 1

Answer: (B)

$x_{A}=6t-3$
$v_{A}=\frac{d}{d t}\left(6 t - 3\right)=6$
Particle A moves with constant velocity.
$v_{B}=\frac{d}{d t}\left(4 t^{2} - 2 t + 3\right)=8t-2, \, \, a_{B}=\frac{d}{d t}\left(8 t - 2\right)=8$
Particle B moves with constant acceleration
$v_{C}=\frac{d}{d t}\left(3 t^{3} - 2 t^{2} + t - 7\right)=9t^{2}-4t+1$
$a_{C}=18t-4$
So, the particle moves with variable acceleration.
$x_{D}=7cos 60^{o} - 3 sin ⁡ 30^{o} \, $
Since $x_{D}$ does not depend upon time therefore particle is at rest.