I am not sure how to solve the following questions (answers are provided). Could

Question

I am not sure how to solve the following questions (answers are provided).

Could someone please show me how to get the following answers?

An object with a mass of 2 kg is found to be moving in the x-direction such a way that its position has the following time dependence: x(t) = 5t^2 (where x and t are in SI units of m and s, respectively)

a). How much work would be required to slow the object back down to the velocity it had at t = 0s?

     Ans). -2500 J

b). If the initial potential energy of the object (at t = 0 s) is 10 J, what is the value of its potential energy at t = 5s?

     Ans). -2490 J

Explanation / Answer

x(t) = 5t^2

v=10t

a=10

distance covered in that time=125m

work= f*displacement=2*10*125=-2500j

2)at t=0 Pe=10J

at t=5 sec

v= 50m/s

KE=PE=-1/2*2*50^2=-2500 J

Total PE=-2500+10=-2490 J

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