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The acceleration of a particle is increa...

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity `v_0`. The distance travelled by the particle in time t will be

A

`nu_(0)t+(1)/(3) bt^(2)`

B

`nu_(0)t +(1)/(3) bt^(3)`

C

`nu_(0)t+(1)/(6)bt^(3)`

D

`nu_(0)t+(1)/(2)bt^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Acceleration `a= (dv)/(dt) = bt` , so , dv= btdt
Integrating equation (i) within the conditions of motion we have ,
`int_(nu_(0))^(nu)dnu=int_(0)^(t)"btdt or "(nu-nu_(0))=(bt^(2))/(2)`
or `nu=nu_(0)+(bt^(2))/(2)=(ds)/(dt) " or ds " = nu_(0)dt +(bt^(2))/(2) `dt
Integrating equation (ii) we get s =` nu_(0)t +(1)/(6) bt^(3)`
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