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its very simpe brodiff it you will get t^2
put t=2 in it you will get 4 thats v
the use Ke=1/2mv^2 =1/2x2x4x4 =16This is your answer :)
differentiate it once to get velocityat t=o and t=2sec, uget u=0and v=4 m/s .apply we theorem to get work done =4N
sorry, calculation mistake answer would become 16N
a=2t and dx = t^2dt
hence f=2*2t=4t
dw=f.dx=4t*t^2dt=4t^3dt
integrating
=t^4 from 0 to 2
=16 joules
As x is a function of time we can get the distance the body has travelled in the first two seconds. The one which u did to find acceleration of the body is right. As the force is 8N the displacement of the body is 8/3 so the work done is 64/3J. Or u can try it in another method. As u got the acceleration in terms of t which is 2t so F(t) is 4*2t which is 8t. Work by definition means F.dx. Find dx which we get it as t^2 dt now multiply F(t) with t^2 dt and integrate it by putting limits from 0 to 2 and now u will get the right answer which is 64/3J. Second way is a professional way of doing problems.
Hope this helps u.
16
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