Question

The displacement of a body moving along a straight line is given by: $S=b{t}^n$, where ${}^{\prime }{b}^{\prime }$ is a constant and ${}^{\prime }{t}^{\prime }$ is time. For what value of ${}^{\prime }{n}^{\prime }$ the body moves under the action of constant force?

• A. 3/2
• B. 1
• C. 2
• D. 1/2

Answer 1

The correct option is C 2

Force $=$ mf
$=$ mass $\times$ acceleration
$=mf$
$=m\frac{d^{2}S}{d{t}^2}$

$=m\frac{d^2}{d{t}^2}\left(b{t}^n\right)$

$=mnb\frac{d}{dt}\left(t^{n-1}\right)$

$=mnb(n-1)t^{n-2}$

Since force is constant, so, $n=2$.