Question

A constant force of $5N$ is applied continuously on a body of mass $10kg$ for $4$ seconds. The body moves $800cm$ along a straight line. What is the velocity of the body when the force was applied initially?

Answer 1

Hint : When $F$ force is applied on a body of mass $m$ , the acceleration of body $a=\dfrac{F}{m}$ . Acceleration of a body $=\dfrac{final\,velocity\,-\,initial\,velocity}{\Delta t}$
Equation of motion:- $20s={{v}^{2}}-{{u}^{2}},s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where $a=$ acceleration
$s=$ displacement
$v=$ find velocity
$u=$ initial velocity.

Complete Step By Step Answer:
Given that force applied $F=SN$
Mass of body $m=10kg$
Duration of force applied $t=4\sec$
Displacement of body $s=8m$
We know $ac{{c}^{n}}$ of body $a=\dfrac{F}{m}=\dfrac{5}{10}=0.5m/{{s}^{2}}$
We have $s,a,t$ and we need to find out $u$ .
Now we will choose the suitable equation of motion $s=ut+\dfrac{1}{2}a{{t}^{2}}$
By putting the value of $s,a$ and $t$
$\Rightarrow ut+\dfrac{1}{2}\left( 0.5 \right){{t}^{2}}=8$
$\Rightarrow u\left( 4 \right)+\dfrac{1}{2}\left( 0.5 \right){{\left( 4 \right)}^{2}}=8$
$\Rightarrow 4u+4=8$
$4u=4$
$u=1m/s$
Therefore initial velocity of object $=1m/s$ .

Note :
Students should select the suitable equation of motion. Otherwise they will reach a correct answer but time taken will be made to solve the question.
For example if some choose $2as={{v}^{2}}-{{u}^{2}}$ to solve this question. Here are two unknown variables ( $v$ and $u$ ). Now students will have to first find $V$ from the first equation of motion $v=u+at$ . Ultimately answers will be obtained but steps will increase, so always choose the equation in which the unknown are minimum.
There equation of motions:
$v=u+at$
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
$2as={{v}^{2}}-{{u}^{2}}$ .