Question

It takes a minimum distance of 57.46 m to stop a car moving at 13.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 29.0 m/s.

Answer 1

The minimum stopping distance when the car is moving at

29.0 m/sec = 285.94 m

Step-by-step explanation:

We know by equation of motion that,

`v^(2)=u^(2)+2\cdot a \cdot s`

Where, v= final velocity m/sec

u=initial velocity m/sec

a=Acceleration m/
`Sec^(2)`

s= Distance traveled before stop m

Case 1

u= 13 m/sec, v=0, s= 57.46 m, a=?

`0^(2) = 13^(2) + 2 \cdot a \cdot57.46`

a = -1.47 m/
`Sec^(2)` (a is negative since final velocity is less then initial velocity)

Case 2

u=29 m/sec, v=0, s= ?, a=-1.47 m/
`Sec^(2)` (since same friction force is applied)

`v^(2) = 29^(2) - 2 \cdot 1.47 \cdot S`

s = 285.94 m

Hence the minimum stopping distance when the car is moving at

29.0 m/sec = 285.94 m