body's initial speed amounts 72 km/h and it is gradually slowing down due to the friction. If the coefficient of friction amounts 0.5 what distance will the body cross before it stops? g=10 m/s2

Answer 1

Let

v = 72 km/h = 72000m/3600s = 20 m/s be the initial velocity,

f = 0.5 be the coefficient of friction,

g = 10 m/s² be gravitational acceleration,

m be the (unknown) mass of the body.

(I think the point of this exercise is to show that the answer is independent of m;

that is why the mass is not given.)

In the absence of any information about the surface, I assume that it is horizontal.

Under that assumption the force of friction is

F = mgf

By Newton's Second Law the body experiences deceleration

a = F/m = gf

By definition of acceleration the body will stop in time

t = v/a

During that time it will traverse the distance

s = at²/2 = av²/2a² = v²/2a = v²/2gf

Substituting actual numbers

s = 20²/(2×10×0.5) = 40 m