Question

The position of a particle travelling along x - axis is given by $x_t$ = $t^3$ - 9 $t^2$ + 6t where $x_t$ is in m and t is in second . Then

1) the particle does not come to rest at all.

2) the particle comes to rest firstly at (3 - $\sqrt{7}$ ) s and then at (3 + $\sqrt{7}$) s

3) the speed of the particle at t= 2s is 18 m$s^{-1}$

4) the acceleration of the particle at t= 2s is 6 m$s^{-2}$

• A. 2,3, 4 are correct
• B. 2,3 are correct
• C. All of them are correct
• D. 1 and 2 are correct

Answer 1

The correct option is A

2,3, 4 are correct

$x_t$ = $t^3$ - 9 $t^2$ + 6t

v= $\frac{d{x}_t}{dt}$ = (3 $t^2$ - 18t + 6) m $s^{-1}$

So, the particle comes to rest since this equation has two valid roots.

$\Rightarrow$ $t_1$ = (3 - $\sqrt{7}$) s and $\Rightarrow$ $t_2$ = (3 - $\sqrt{7}$) s

Substituting the value t = 2s in the equation for velocity, we get, v= = - 18 m$s^{-1}$

The acceleration of the particle is a=6t - 18 m$s^{-2}$

Substituting the value t = 2s in the equation for acceleration, we get, a= = - 6 m$s^{-2}$