Question

# The velocity of a particle moving along a straight line increases according to the linear law v = v0 + kx where k is a constant . Then 1) the accelearation of the particle is k(v0 + kx) 2) the particle takes a time 1k loge (v1v0) to attain a velocity v1 3) velocity varies linearly with displacement with slope of velocity displacement curve equal to k 4) data is insufficient to arrive at a conclusion.

A

1,2,3 are correct

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B

2,3 are correct

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C

all of them are correct

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D

1 and 2 are correct

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Solution

## The correct option is A 1,2,3 are correct Options (1), (2), (3) are correct. Accelearation = dvdt =kv ⇒ a = k (v0 + kx) Further ⇒ dvdt = kv ⇒ dvv = kdt v1∫v0 dvv = k t∫0 ft t = 1k loge v1v0 Since , v = v0 + kx . Hence slope of velocity displacement curve is dvdx = k

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