A body is travelling in a straight line path with a velocity given by v = ax where 'a' is a constant such that a = 5 units. What will be the work done by the force acting during its displacement from x = 0 to x = 2m ?

Options

A. 15 J
B. 50 J
C. 10 j
D. 100 J

Answer

b

Explanation

Here `v=a x^(3//2)`
Differentiating `(dv)/(at)=3//2a x^(1//3)(dv)/(dt)`
or `a=3//2a.x^(1//2)xxv`
=`3//2a x^(1//2)xx ax^(3//2)`
=`3//2^2x^2`
`:.` Force `F=ma=3//2a^2 x^2xx0.5`
=`3//4a^2x^2`
Now Work `W=int_0^2 F dx=int_0^2 3//4a^2x^2dx`
=`3//4a^2[x^3/3]_0^2`
=`3//4xx(5)^2xx8//3=50 J`