Question

At a place where the acceleration due to gravity is $10m{{s}^{-2}}$, a force of $5Kg-wt$acts on a body of mass $10Kg$ initially at rest. The velocity of the body after 4 seconds?
A. $5m{{s}^{-1}}$
B. $10m{{s}^{-1}}$
C. $20m{{s}^{-1}}$
D. $50m{{s}^{-1}}$

Answer 1

A constant force is acting on the body. This implies that the acceleration of the body is constant and that it is experiencing an equal amount of increase in velocity per unit time. Hence, the body is going under uniformly accelerated motion. Moreover, the three equations of uniformly accelerated motion can be used for calculating the final velocity of the body.

Complete step-by-step solution:
Given that force of 5 Kg-wt acts on the body while it is at rest.
Force on a body is expressed as:
$\vec{F}=m.\vec{a}$
Where,
$\vec{F}=$ force on the body
$m=$ mass of the body
$\vec{a}=$ acceleration of the body

The S.I. unit of force is Newton but it's another unit is Kg-Wt.
1 Newton = 10 Kg- Wt
Here, $F=5Kg-wt=50N$and $m=10Kg$
$\Rightarrow a=\dfrac{F}{m}$
$\begin{aligned} & \Rightarrow a=\dfrac{50}{10} \\\ & \Rightarrow a=5m{{s}^{-2}} \\\ \end{aligned}$

Now, using the first equation of motion, $v=u+at$
Where,
$v=$ final velocity
$u=$ initial velocity $=0m{{s}^{-1}}$ (the body is at rest initially)
$t=$ time duration $=4s$
$\begin{aligned} & \Rightarrow v=0+\left( 5 \right)\left( 4 \right) \\\ & \Rightarrow v=20m{{s}^{-1}} \\\ \end{aligned}$

Therefore, the correct option is (C) $20m{{s}^{-1}}$.

Note:
When a body is going under non uniformly accelerated motion, the three equations of motion cannot be used to calculate the velocity, time taken, displacement or acceleration of the body. We have to use the differential equations of motion to determine these quantities in a non uniformly accelerated motion. This is because the changes at infinitesimal small instances of time are to be determined as well which is not possible using the simple equations of motion.