Question

Question #a7378

Answer 1

(b)

Explanation:

The car accelerates from rest with an acceleration of # alpha# for a time `t_1`.
velocity after time `t_1` is given by the expression
`v=u+at`
Inserting given values we have
`v=0+alphat_1`
`=>v=alphat_1` .......(1)
Thereafter it is decelerated at a rate `beta` for a time `t_2` when it comes to halt.
We have
`0=v-betat_2`
`=>v=betat_2` .....(2)
Total time `t_1+t_2=t`
`=>t_2=t-t_1`
Inserting in (2) we get
`v=beta(t-t_1)` ......(3)
From (1) we have `t_1=v/alpha`. Inserting in (3) above
`v=beta(t-v/alpha)`

Solving for `v`, we have

`v+beta/alphav=betat`
`=>v(1+beta/alpha)=betat`
`=>v=(betat)/(1+beta/alpha)`
`=>v=(alphabetat)/(alpha+beta)`