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A car accelerates from rest at a constan...

A car accelerates from rest at a constant rate `alpha` for some time, after which it decelerates at a constant rate `beta,` to come to rest. If the total time elapsed is t seconds. Then evalute (a) the maximum velocity reached and (b) the total distance travelled.

A

`V=t(alphabeta)/(alpha-beta)`

B

`V=t((beta^(2))/(alpha-beta))`

C

`V=t((alpha^(2))/(alpha+beta))`

D

`V=t((alphabeta)/(alpha+beta))`

Text Solution

Verified by Experts

The correct Answer is:
D
`t=t_(1)+t_(2)`
slope of `OA` curve `=tantheta=alpha=(v_(max))/(t_(1))`
slpe of `AB` curve `=beta=(v_(max))/(t_(2))`

`rArrt=(v_(max))/(alpha)+(v_(max))/(beta)rArrv_(max)=((alphabeta)/(alpha+beta))t`
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