Question

A car is traveling at when the driver sees an accident m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup?

Answer 1

Deceleration =
`(v^2)/(2a)` units/sec^2

Explanation:

Given that a car is traveling at when the driver sees an accident m ahead and slams on the brakes.

i.e. if he is coming with speed v units/sec say, he has to make his velocity 0.

Distance travelled = m units

Initial velocity = v

Final velocity =0

Use the third formula as

`v^2=u^2+2as\\0=v^2+2am\\a =(-v^2)/(2a)`

So he has to apply an acceleration of
`(-v^2)/(2a)` units/sec^2 to stop the car in time to avoid a pile up.

Deceleration =
`(v^2)/(2a)` units/sec^2