Question

A force applied for a duration of 10 seconds on a body of mass \[5kg\] is initially at rest. As a result the body acquires a velocity of \[2m{s^{ - 1}}\]. Find the magnitude of the force applied.
(A) \[1N\]
(B) \[2N\]
(C) \[4N\]
(D) \[5N\]

Answer 1

Hint: According to the given question, we can see that a force applied for a particular period of time has caused the body to move. Using the given data and by applying equations of motion, we can find acceleration and hence the force using Newton’s second law.

Complete Step by Step Answer:
It is given that a force is applied on to a body of mass \[5kg\], which is said to be at rest initially. Now, as a result of this force, the body is set to accelerate with a velocity of \[2m{s^{ - 1}}\]. Now, look at the given data carefully, we know velocity of the object post the force is applied on to it , we know that the body was initially at the state of rest and we know the time period that the force is applied. Using these, we can opt for motion equations, where we can find acceleration value , which is essential to calculate the magnitude of force.
Using the given data, we can find the body’s acceleration using first equation of motion given by
\[ \Rightarrow v = u + at\]
Now, we know that the initial velocity of the object is zero since the object is said to be in rest. Substituting the known values we get,
\[ \Rightarrow 2 = 0 + a(10)\]
\[ \Rightarrow a = 0.2m{s^{ - 2}}\]
Now, using Newton’s second law , we know that force is directly proportional to the acceleration of the body, suing this we get,
\[ \Rightarrow F = ma\]
Substituting known values we get,
\[ \Rightarrow F = (5)(0.2)\]
\[ \Rightarrow F = 1N\]

Hence, the magnitude of force is equal to 1 N. Thus, option (A) is the right answer.

Note: Newton’s second law of motion states that the acceleration of the body which is produced by a net force of a particular magnitude is directly proportional to the magnitude of net force applied on the object.