Question

What is the formula for average force?

Answer 1

Hint: The average force is the product of mass and the average velocity. The average velocity is the difference between the initial and final velocities of a body. Thus, the average velocity is the product of mass and change in velocity by the change in time.
Formula used:
$$F=ma$$

Complete step-by-step solution:
The force is a vector quantity and even the average force is also a vector quantity, that is, it has both magnitude and direction.
The basic definition of force is the product of acceleration and mass. So, we have,
$$F=ma$$
Where m is the mass and a is the acceleration.
The acceleration is the rate of change of velocity, that is,
$$a={\displaystyle \frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}}$$
Where $$\mathrm{\Delta }v$$is the change in velocity and $$\mathrm{\Delta }t$$ is the change in time.
Replace the expression of the acceleration in place of the term ‘a’.
$$F=m\left({\displaystyle \frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}}\right)$$
Where m is the mass, $$\mathrm{\Delta }v$$is the change in velocity and $$\mathrm{\Delta }t$$ is the change in time.
Or we can rewrite the above expression as follows.
$$F=m\left({\displaystyle \frac{v-u}{\mathrm{\Delta }t}}\right)$$
Where m is the mass, v is the final velocity, u is the initial velocity and $$\mathrm{\Delta }t$$ is the change in time.
The above expression defines force as the product of mass and change in velocity per time.
$$\therefore$$ The formula for the average force is $$F=m\left({\displaystyle \frac{v-u}{\mathrm{\Delta }t}}\right)$$ with m being the mass, v being the final velocity, u being the initial velocity and t being the change in time.

Note: The average force can be used to compute the impulse. The average force is inversely proportional to the change in time, that is, if the average force doubles, then, the time reduces exactly by half the value.