Question

A constant force acting on a body of mass 3.0kg changes its speed from $2.0\ m{{s}^{-1}}$ to $3.5\ m{{s}^{-1}}$ in 25s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

Answer 1

Hint:
The force acting on a body is given by: $F=ma$. Using the motion law of: $v=u+at$, the value of the acceleration (a) can be found. Using this value, we can find the magnitude of the force. The direction of the force can be found by finding the direction of the motion of the body.

Step by step solution:
As per the problem, we are given a body of mass 3.0kg. This body is having an initial velocity of $2.0\ m{{s}^{-1}}$. The final velocity of this body is $3.5\ m{{s}^{-1}}$. The amount of time taken to attain the final velocity of $3.5\ m{{s}^{-1}}$ is 25s. To find the value of acceleration, we will use the motion law of: $v=u+at$.
Putting in the values of the problem, that is: u=$2.0\ m{{s}^{-1}}$, v=$3.5\ m{{s}^{-1}}$ and t=25s, we will find the value of acceleration to be: $v=u+at\Rightarrow 3.5=2.0+a(25)\Rightarrow \dfrac{3.5-2.0}{25}=a\Rightarrow a=\dfrac{1.5}{25}=0.06m{{s}^{-2}}$.
Therefore the body accelerates with an acceleration value of $a=0.06m{{s}^{-2}}$.
Now, to find the value of the force acting on the body, we will use the general formula of force, given by: $F=ma$.
We already have the value of the mass of the body given be: m=3.0kg. Further, the value of acceleration as we found out earlier is: $a=0.06m{{s}^{-2}}$.
Hence, the amount of force acting on the body will be: $F=ma\Rightarrow F=3.0\times 0.06=0.18N$.
Therefore, the value of the magnitude of the force acting on the body is 0.18N.
Now, we will use another piece of information given that is, the direction of the motion of the body remains unchanged. Hence, the direction of the force acting on the body will remain the same as it was towards the initial direction of motion of the body.

Note:
Since, the direction of the force acting on the body remains unchanged, hence the angle between the initial force of the body and the force acting on the body is ${{0}^{0}}$. To understand it better, consider a football moving toward forward direction, a player sprints upto the ball and kicks it forward in the same direction. This is the scenario as in the problem.
Now, if the player was to kick the ball in another direction by kicking the ball at an angle using the same amount of force as in the previous case, then the magnitude of the force on the ball would remain the same, however the direction of the force and hence the direction of motion of the ball would change.