A force F acts on a stationary body for the time t. The distance covered by the body 'S' will be proportional to:a)tb)1/tc)t2d)1/t2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

S=ut+1/2at^2 Since the mass is constant, and i guess you dont mean above to be dealt in relativistic speed, and a constant force is applied then we will have constant acceleration. So distance covered will be only dependent on elapsed time t.So s ∝ t^2

Answer

We are said that a Force F acts on a stationary body for time t.
Since a constant Force is acting, the body has constant acceleration for time t. In other words, the motion of body is uniformly accelerated for time t.
If the mass of the body is m, then we have. F= ma
a=F/m

Thus, an acceleration a acts on the body for time t. Now we can find the distance s covered by the body in this time.
Also, the body was initially stationary. So initial velocity is zero.
We use the following equation of motion:

s=ut+/at^2
s=(0)t +1/2×F/M×t^2 s= F/2m×t^2. s proportinal to t^2

Answer

Explanation:
When a force is applied on a stationary body, it causes the body to accelerate. The distance covered by the body is proportional to the square of the time for which the force is applied. Let's understand this in detail:

Newton's Second Law of Motion:
According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. It can be expressed as:

F = ma

Where:
F = Force applied on the object
m = Mass of the object
a = Acceleration produced in the object

Equation of Motion:
The equation of motion that relates distance (S), initial velocity (u), time (t), and acceleration (a) is:

S = ut + (1/2)at^2

In this case, the body is initially at rest, so the initial velocity (u) is zero. Therefore, the equation becomes:

S = (1/2)at^2

Proportional Relationship:
As we can see, the distance covered by the body (S) is directly proportional to the square of the time (t^2) for which the force is applied. This means that if we double the time, the distance covered will become four times. Similarly, if we triple the time, the distance covered will become nine times, and so on.

Correct Answer:
Therefore, the correct answer is option 'C' (t^2), as the distance covered by the body is proportional to the square of the time for which the force is applied.

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