Question

A force of 500 N acts on a body of mass 1000 kg and the body is brought to rest within a distance of 64 m. Find the initial velocity and the time taken by the body before to come to rest.

• A. $8{ms}^{-1}$,$16s$
  
• B. $8{ms}^{-1}$,$18s$
• C. $16{ms}^{-1}$,$16s$
• D. $8{ms}^{-2}$,$16s$

Answer 1

The correct option is A $8{ms}^{-1}$,$16s$

Solution: Force, F= 500 N ; mass of the body, m= 1000 kg.
From newtons second law of motion,
F = ma, where F, m and a are the force , mass and acceleration respectively.
$a=\frac{F}{m}=\frac{500}{1000}=0.5{ms}^{-2}$
To find initial velocity , consider the equation of motion $v^2=u^2+2$ as
Since the body is retarding $a=-0\times 5{ms}^{-2}$ and since it comes to rest v =0
$\therefore 0=u^2+(2\times (-0\times 5)\times 64)0=u^2-(1\times 64)\Rightarrow u^2=64\Rightarrow u=\sqrt{64}=8{ms}^{-1}Tofindthetimetaken,considertheequationofmotionv=u+at0=8-0\times 5\times t\Rightarrow t=\frac{8}{0.5}=16s\therefore u=8{ms}^{-1},t=16sanda=-0\times 5{ms}^{-2}$