Question

A body starts from origin and moves along x - axis such that at any instant velocity is $v_t$ = 4 $t^3$ - 2t where t is in seconds $v_t$ is m $s^{-1}$ .

The acceleration of the particle when it is 2 m from the origin is 11 x m $s^{-1}$ , where x is

• A. 3
• B. 2
• C. 7
• D. 0

Answer 1

The correct option is B

2

$v_t$ = 4 $t^3$ - 2t

$\Rightarrow$ $\frac{d{x}_t}{dt}$ = 4 $t^3$ - 2t

$\Rightarrow$ $\int$ d$x_1$ = $\int$ 4 $t^3$ dt - $\int$ 2t dt

$\Rightarrow$ $x_1$ = $t^4$ - $t^2$

Since , $x_1$ = 2m

$\Rightarrow$ t = $\sqrt{2s}$ [Rejecting negative time]

Now acceleation is

$a_t$ = $\frac{d{v}_t}{dt}$ = 12 $t^2$ - 2 = 12(2) - 2 = 22 m $s^{-2}$