Question

An automobile is traveling at 60km/h can brake to stop at 20m distance if the car is going at 120km/h then what will be the stopping distance?

Answer 1

`80\ m`

Explanation:

Assumption: The resisting force on car is independent of the velocity.

Let `a` be the deceleration of car when brake is applied to cause the car moving with initial velocity `u=60\ \text{km/hr}=50/3\text{m/s}` to stop (final velocity, `v=0`) at `s=20\ m` distance.

Now, using third equation of motion

`v^2=u^2+2as`

`0^2=(50/3)^2-2a(20)`

`a=125/18`

If `s` is the distance traveled by car travelling with initial velocity `u=120\ \text{km/hr}=100/3\text{m/s}` up to dead stop when final velocity, `v=0` under deceleration `a=125/18 \ text{m/s}^2`.

Now, using third equation of motion

`v^2=u^2+2as`

`0^2=(100/3)^2-2(125/18)s`

`s=10000/125`

`s=80`

Hence the car will travel a distance `80\ m` up to dead stop