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The velocity 'v' of a particle moving al...

The velocity `'v'` of a particle moving along straight line is given in terms of time `t` as `v=3(t^(2)-t)` where `t` is in seconds and `v` is in `m//s`.
The distance travelled by particle from `t=0` to `t=2 `seconds is `:`

A

`2m`

B

`3m`

C

`4m`

D

`6m`

Text Solution

Verified by Experts

The correct Answer is:
B
The velocity of particle changes sign at `t=1 sec.`
`:. ` Distance from `t=0` to `t=2 sec. `is `=underset(1)overset(0)int vdt+underset(2)overset(1)int v dt`
`=[(t^(3)-(3)/(2)t^(2))]_(0)^(0)+[(t^(3)-(3)/(2)t^(2))]_(2)^(1)=3m`
Displacement from `t=0` to `t=2sec. ` is `underset(0)overset(2)int v dt`
`=[(t^(3)-(3)/(2)t^(2))]_(0)^(2)=2m`.
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