Question

A vehicle of mass 840 kg pecorre a straight and level road at 72 Km / h. Suddenly, the brakes are applied reducing the speed to 36 km / h. Calculate: a)
A vehicle of mass 840 kg pecorre a straight and level road at 72 Km / h. Suddenly, the brakes are applied reducing the speed to 36 km / h. Calculate:

a) The work of the force exerted by the brakes on the variation of speed

b) The force applied by the brakes

Answer 1

m = 840 kg         u = 72 * 5 / 18 = 20 m/s              v = 36 * 5 /18 = 10 m/s
average deceleration = (v-u) / t = 10 / t
force by breaks = m a = 8400 / t
Impulse exerted by breaks = 8400 N-sec
work by force = change in K.E. = 0 - 1/2 * 840 * (20*20 - 10*10) = - 126000 J
                     = same as force exerted * distance traveled

Answer 2

Mass = 840 kg,  
Initial velocity = 72 km/hr = 72 × 5/18 = 20 m/s          
Final Velocity = 36 km/hr = 36× 5/18 = 10 m/s
Let time be t.
Acceleration = (v-u)/t = (20-10)/t = 10 / t
Force by the brakes = Mass × Acceleration = (840×10/t) = 8400/t
Force exerted by breaks = 8400 N/sec (answer a)

Work by force = Change in Kinetic Energy
= 0-1/2 ×840×(20×20-10×10) =  -126000 Joules (answer b)