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The velocity of a particle along a strai...

The velocity of a particle along a straight line increases according to the linear law `v=v_(0)+kx`, where k is a constant. Then

A

The acceleration of the particle is `k(v_0+kx)`

B

The particle takes a time `1/k` In`((V_1)/(V_1))` to attain a speed of v

C

Velocity varies linearly with displacement with slope of velocity-displacement curve equal to k

D

Data is In suffiecent to arrives at a conclusion.

Text Solution

Verified by Experts

The correct Answer is:
a,b,c
`(dv)/(dt)=k(dx)/(dt)`
`implies(dv)/(dt)=a=kv=k(v_0+kx)`
Further a=`(dv)/(dt)=kv`
`int_(v_0)^(V_1)=kint_(0)^(t)dt`
`t=(1)/(k)`In`((v_1)/(v_0)`
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