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Question

A particle starts from x=0 and moves along a straight line such that its velocity v depends on position x as v=x+4. For the first four seconds, average velocity of the particle (in m/s) is

A
e4+1
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B
e41
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C
e4+4
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D
e44
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Solution

The correct option is B e41
Given, v=x+4
dxdt=x+4
Integrating on both sides
dxx+4=dt
ln(x+4)=t+C
x+4=e(t+C)
At t=0, x=0
x=4et4
v=4et>0 for t>0
Total distance=Total displacement
∴ Average velocity for first 4 seconds =Total displacementTotal time
=4e444=e41

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