Momentum can be defined as the product of mass and velocity. It is denoted by "p" and its S.I unit is Kgms^-1. Momentum is a vector quantity. $$ p = mv $$ where, $$ m = \text{mass in kg} $$ $$ v = \text{velocity in m/s} $$

Impulse can be defined as the product of force acting on a body and the time it takes to act. It is denoted by "I". Its S.I unit is Ns. $$ I = Ft $$ where, $$ F = \text{force in N} $$ $$ t = \text{time in s} $$

Example 1: A constant force of 5N acts for 5s on a mass of 5kg initially at rest. Calculate the final momentum (WAEC)

$$ p = mv $$ $$ m = 5kg $$ $$ t = 5s $$ $$ F = 5N $$ $$ u = 0 $$ To solve for momentum, we must first find the value for v;
But, $$ F = ma $$ $$ a = \frac{F}{m} = \frac{5}{5} $$ $$ a = 1m/s² $$ Also, from the equations of motion $$ v = u + at $$ $$ v = 0 + 1 × 5 $$ $$ v = 5m/s $$ $$ \therefore p = 5 × 5 $$ $$ \text{final momentum} = 25\text{ kgm}{s^{-1}} $$

Example 2: A 20g bullet moving at 200m/s hits a bag of sand and comes to rest in 0.011s. What is the momentum of the bullet just before hitting the bag? Find the average force that stopped the bullet.

$$ m = 20g = 0.02kg $$ $$ \text{initial velocity} = 200m/s $$ $$ t = 0.011s $$ $$ \text{final velocity} = 0 $$ The momentum, p is given by; $$ p = mv $$ $$ p = 0.02 × 200 $$ $$ p = 4 \text{kgm/s} $$ To calculate the force, we need to first find the value for acceleration $$ v = u + at $$ $$ 0 = 200 + 0.011a $$ $$ -200 = 0.011a $$ $$ a = \frac{-200}{0.011} $$ $$ a = (-)18181.8 m/s² $$ The -ve sign it was a deceleration since the body came to rest $$\therefore f = ma $$ $$ f = 0.02 × 18181.8 $$ $$ f = 363.3N $$

Example 3: A stationary ball is hit by an average force of 50N for a time of 0.5s. What is the impulse experienced by the ball?