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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

v1v0 dvv = k t0 ft

t = 1k loge v1v0

Since , v = v0 + kx . Hence slope of velocity displacement curve is dvdx = k


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