Question

Try to identify the number of times the velocity of ball changes "A football player kicks a football to another player who kicks towards the goal. The goalkeeper of the opposite team collects the ball and kicks it towards a player of his own team." Also identify the agent supplying the force in each case.

Answer 1

In this question, the concept of Newton’s law of motion will be used that is if a force is applied in an object, it develops an acceleration which is directly proportional to the amount or magnitude of net force applied on the object, and its movement will be in the same direction as of the applied force, and acceleration is inversely proportional to the mass of the concerned object.

Complete step by step solution:
As we know that the force applied on an object can be expressed as,
$\Rightarrow F = \dfrac{{d\left( {mv} \right)}}{{dt}}$
Where, $F$ is the applied force and $d\left( {mv} \right)$ is small change of momentum ( $m$mass multiplied by $dv$ change in velocity) with respect to change in time $dt$. Assuming the mass as constant, the relation of change of velocity is directly proportional to the amount of force applied. This concept helps answering the question.

In the first case, the velocity of the ball changes when the first player kicks the ball towards another player, this is the $1$ time that velocity change occurs.

The velocity of the ball changes again when the player kicks the ball towards the goal. So, the velocity change happens for $2$ times until now.

The next case, the goalkeeper collects the ball, this time its velocity is reduced as it is getting stopped by the goalkeeper, so the velocity change happens for $3$times now.

Finally, the goalkeeper kicks the ball towards his own teammate, so here the velocity again builds up and velocity change occurs for $4$ times totally in this given situation.

First time the agent of force is the first player, second time the agent is second player, third time the agent hands the goalkeeper as he collects it with both of his hands and fourth time or the last time the agent is the foot of the goalkeeper as he kicks it.

Note: As we know that force and velocity are the vector quantities which depend on the direction and the magnitude. If one of the components is changed that is either magnitude or the direction, the velocity and force will change their significance.