Question

A particle is moving in a straight line. At time $t$, the distance between the particle from its starting point is given by $x=t-6t^2+t^3$. Its acceleration will be zero at

• A. $t=1$ unit time
• B. $t=2$ unit time
• C. $t=3$ unit time
• D. $t=4$ unit time

Answer 1

The correct option is B $t=2$ unit time

Given curve is
$x=t-6t^2+t^3$
On differentiating with respect to $x$, we get
$\frac{dx}{dt}=1-12t+3t^2$
Again, differentiating, we get
$\frac{d^{2}x}{d{t}^2}=-12+6t$
When $\frac{d^{2}x}{d{t}^2}=0\Rightarrow t=2$ unit time