Question

A particle starts moving rectilinearly at time t = 0 such that its velocity v changes with time t according to the equation `v = t^2-t`, where t is in seconds and v is in `m s^(-1)`. The time interval for which the particle retrads (i.e., magnitude of velocity decreases)is
A. `t lt 1//2`
B. `1//2 ltt lt1`
C. `tgt1`
D. `tlt1//2 and tgt1`

Answer 1

Correct Answer - B
b. ` v= t^2-t rArr a = 9dv)/(dt) = 2t - 1 `
For retardation, `avlt0`
`rArr (t^2-t)(2t-1)lt0`
` rArr t(t-1)(2t-1)lt0`
This is possible for `1/2lttlt1`.