A car is moving with a uniform velocity of 30 m s^-1. It is stopped in 2 s by applying a force of 1500 N through it's brakes. Calculate (a) the change in momentum of car, (b) the retardation produced in car, and (c) the mass of the car.

(i) We know that,

acceleration = $\dfrac{v - u}{t}$

Given,

v = 0

u = 30 m s^-1

t = 2 s

f = 1500 N

Substituting the values in the formula above we get,

$a = \dfrac{0 - 30}{2} \\[0.5em] \Rightarrow a = - 15 \text{m s}^{-2} \\[0.5em]$

The negative sign shows that it is retardation. So retardation = 15 m s ^-2

Now,

Force (f) = mass (m) x acceleration (a)

Substituting the values in the formula above we get,

$1500 = m \times (15) \\[0.5em] \Rightarrow m = 100 \text{kg} \\[0.5em]$

Hence,

Mass of the car = 100 kg

As we know,

Change in momentum = Final momentum - Initial momentum

Initial momentum = mu = 100 x 30 = 3000 kg m s^-1

Final momentum = mv = 100 x 0 = 0

Substituting the values in the formula above we get,

Change in momentum = 0 - 3000 = - 3000 kg m s^-1

Hence,

(i) change in momentum = 3000 kg m s^-1

(ii) The retardation produced in the car = 15 m s ^-2

(iii) The mass of the car = 100 Kg