Question

A vehicle of mass m is moving with momentum p on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is µ. The stopping distance is ____________.

(g = acceleration due to gravity)

पर्याय

• `"p"^2/(2µ"m"^2)`

• `"p"^2/(2µ"gm"^2)`

• `"p"^2/(µ"gm"^2)`

• `"p"^2/(2µ"g")`

Answer 1

A vehicle of mass m is moving with momentum p on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is µ. The stopping distance is `underline("p"^2/(2µ"gm"^2))`.

Explanation:

The acceleration of vehicle on a rough horizontal road is

a = µg ...........(i)

where µ = coefficient of friction.

The momentum of vehicle, p = mu

u = `"p"/"m"` .......(ii)

Using third equation of motion,

V² = u² − 2as

As the vehicle stops after distance s, so

0 = u² − 2as

or s = `"u"^2/(2"a")`

s = `("p"/"m")^2/(2(µ"g"))` ...........[using Eqs. (i) and (ii)]

s = `"p"^2/(2µ"gm"^2)`