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A car accelerates from rest at a constan...

A car accelerates from rest at a constant rate a for some time and then decelerates at a constant rate `b` to come to rest. The total time elapsed is `t`.
Total distance travelled by the car is .

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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