Question

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

$x_A=6t-3;x_B=4t^2-2t+3;x_C=3t^3-2t^2+t-7;$ $x_D=7cos60^o-3sin30^o$

The particle moving with constant acceleration is

• A. A
• B. B
• C. C
• D. D

Answer 1

Answer: (B)

$x_A=6t-3$
$v_A=\frac{d}{dt}\left(6t-3\right)=6$
Particle A moves with constant velocity.
$v_B=\frac{d}{dt}\left(4t^2-2t+3\right)=8t-2,a_B=\frac{d}{dt}\left(8t-2\right)=8$
Particle B moves with constant acceleration
$v_C=\frac{d}{dt}\left(3t^3-2t^2+t-7\right)=9t^2-4t+1$
$a_C=18t-4$
So, the particle moves with variable acceleration.
$x_D=7cos60^o-3sin30^o$
Since $x_D$ does not depend upon time therefore particle is at rest.