a block is moving with a velocit v on a straight surface what is the shortest distsnce and shortest time the block can be stopped

Question

this is a question of friction i want the answer

 

Answer 1

Assuming a coefficient of kinetic friction μ_k, mass m of the object, and a constant opposing force of friction,

 

f = -μ_kmg

 

v(t) = v + at

 

a = f/m = -μ_kmg/m = -μ_kg

 

Set v(t) = 0 and solve for t.

 

0 = v + at = v - μ_kgt

 

t = v/(μ_kg)

 

Distance to stop:

 

v_f² - v_i² = 2ad

 

0² - v² = -2μ_kgd

 

d = v²/(2μ_kg)