A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate: (i) the velocity acquired by the body, and (ii) change in momentum of the body.

As we know,

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

Given,

f = 10 N

m = 2 kg

t = 3 s

u = 0

Substituting the values in the formula above we get,

$10 = 2 \times a \\[0.5em] \Rightarrow a = \dfrac{10}{2} \\[0.5em] \Rightarrow a = 5 \text {m s}^{-2} \\[0.5em]$

Hence,

Acceleration produced by the body = 5 m s^-2

The 1^st equation of motion states that;

v = u + at

Substituting the values in the formula above we get,

$v = 0 + (5 \times 3) \\[0.5em] \Rightarrow v = 15 \text {m s}^{-1}$

Hence, velocity of the body is 15 m s^-1

(ii) As we know,

Change in momentum = Final momentum - Initial momentum

Initial momentum = mu = 2 x 0 = 0

Final momentum = mv = 2 x 15 = 30 kg m s^-1

Substituting the values in the formula above we get,

Change in momentum = 30 - 0 = 30 kg m s^-1