Question

A particle of mass 12 kg is acted upon by a force f = (100 - 2x2) where fis in newton and x is in
metre. Calculate the work done by this force in moving the particle x=0 to x= - 10 m. What will
be the speed at x = 10 m if it starts from rest?​

Answer 1

Answer:

Work done=333.33 J

Speed of particle=7.45 m/s

Explanation:

Given:

Mass of the particle=12 kg

Force $f=100-2x^2$

Let w  Work done by the given force be w given by

$w=\int f.dx\\=\int (100-2x^2).dx\\=100x-\dfrac{2x^3}{3}\\=100(100-0)-\dfrac{2(1000-0)}{3}\\=333.33\ \rm J$

Using work Energy Theorem work done by all forces is equal to the change in kinetic Energy.

$333.33=\dfrac{mv^2}{2}-0\\333.33=\dfrac{12\times v^2}{2}\\v=7.45\ \rm m/s$

Hence the work done and velocity is calculated.

Answer 2

Answer is here!

Hope this helps you