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}} $ .