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Question

The potential energy U of a particle of mass m=1 kg moving in xy plane is given by U=3x+4y, where x and y are in metre and U is in joule. If initially particle was at rest, then its speed at t=2s will be 


Correct Answer
A
10 m/s
Your Answer
B
6 m/s
Your Answer
C
8 m/s
Your Answer
D
7 m/s

Solution

The correct option is A 10 m/s
Given U=3x+4y,
So Ux=3,Uy=4
We have relation between force and potential energy as 
F=Ux^iUy^j=3^i4^j
|F|=32+42=5 N
From Newtons second law 
ma=5
a=5 ms2(m=1 kg)
As acceleration is constant we can apply equations of motion
V=u+at
At t=2s,
V=0+5(2)=10 ms1.

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