Question

A body of mass 3 kg is under a constant force which causes a displacement s in meters in it, given by the relation s = (\(\frac{1}{3}\)) t², where t is in s. Work done by the force in 2 s is :

• A. (\(\frac{17}{3}\))J
• B. (\(\frac{3}{8}\))J
• C. (\(\frac{8}{3}\))J
• D. (\(\frac{3}{17}\))J

Answer 1

The Correct Option is C

Work Done by Constant Force: The work done by a constant force is given by the formula W = F\(\times\)d, where F is the force and d is the displacement. 
In this case, s = (\(\frac{1}{3}\))t², so the force is F = m\(\times\)(\(\frac{d^2}{dt^2}\)) = \(\frac{2t}{3}\). 
To find the work done in 2 seconds, integrate F with respect to t over the interval [0, 2]: 
W = \(\int_{0}^{2}\) (\(\frac{2t}{3}\)) dt = (\(\frac{2}{3}\))\(\times\)[\(\frac{t^2}{2}\)] from 0 to 2 = (\(\frac{2}{3}\))\(\times\)(\(\frac{2^2}{2}-0\)) = (\(\frac{8}{3}\)) J. 
So, the correct option is (\(\frac{8}{3}\)) J.