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A particle moves in a straight line. its speed increases linearly with time. if the inital speed of the particle is V 0 and it's speed at t=4s is 2V 0 then 0 ∫ 4 v dt is equal to? (ans is 6V 0 ) . Pls explain the answer. thanks in advance

A particle moves in a straight line. its speed increases linearly with time. if the inital speed of the particle is V0 and it's speed at t=4s is 2V0 then 0 ∫ 4 v dt is equal to? (ans is 6V0)
.
Pls explain the answer. 
thanks in advance

Grade:11

1 Answers

Khimraj
3007 Points
5 years ago
v = ct + d
where c and d are constant
at t = 0, v= vo
vo = d
so v = ct + vo
at t=4, v = 2vo
2vo = c*4 + vo
c = vo/4
so v = vo(t/4 + 1)
so \int_{0}^{4}vdt = (v_{o})\int_{0}^{4}(t/4 + 1)dt = 6v_{o}
Hope it clears....................................

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