Question

For a moving body, at any instant of time

(A) If the body is not moving, the acceleration is necessarily zero.

(B) If the body is slowing, the acceleration is negative.

(C) If the body is slowing, the distance is negative.

(D) If displacement, velocity and acceleration at that instant are known, we can find the displacement obtained in the given time in future.

Answer 1

Hint: We will try a concept where a movement of the body is related to acceleration. Thus, basically, we will use Newton’s Second Law. $ F = ma $

Where, $ F $ is the force on the object, $ m $ is the mass of the object and $ a $ is the acceleration of the object.

Complete step by step answer

We will discuss all the options one at a time taking into account Newton's Second Law of Motion. We assume, $ F $ to be the force acting, $ m $ to be the mass of the body, $ a $ to be its acceleration.

Firstly, Let us discuss option (A),

It says that if the body is not moving, the acceleration is necessarily zero.

So,If the body is not moving, that means force acting is $ 0 $ .

Thus, $ F = ma \Rightarrow 0 = ma $ . That means, Either $ m = 0 $ or $ a = 0 $ But For an actual object, mass cannot be zero. Thus,

 $\Rightarrow m \ne 0 $

That means acceleration has to be zero,Hence,

 $\Rightarrow a = 0 $

But if a body is thrown vertically upward then at a point velocity of body will be zero and it will change its direction of motion at that particular point body is not moving but acceleration is not zero as gravitational acceleration is acting on it, so we can it is not necessary that acceleration is zero for a body in rest.

Which means (A) is incorrect.

Now, We will discuss option (B). This says that if the body is slowing, the acceleration is negative. If the body is slowing,

Then, Final force ( $ {F_{final}} $ ) is less than Initial Force ( $ {F_{initial}} $ )

$\Rightarrow {F_{final}} < {F_{initial}} $

We can say,

$\Rightarrow {F_{final}} = m{a_{final}} $ And $ {F_{initial}} = m{a_{initial}} $

Thus, $ m{a_{final}} < m{a_{initial}} $

Thus, Finally we can say,

$\Rightarrow {a_{final}} < {a_{initial}} $

Thus, The net acceleration of the body, $ a = {a_{final}} - {a_{initial}} < 0 $

Thus, (B) is also correct.

Now, we will discuss about option (C) which is about distance, as we know from Newton’s equations of motion that 

$\Rightarrow v^2 = u^2 + 2as $

If the body is slowing then $v < u$ hence $v^2 < u^2$.

Now when the body is slowing that means that acceleration is opposite of the direction of motion.

$\Rightarrow s = \dfrac{v^2 - u^2}{2a}$

$\Rightarrow s = \dfrac{-ve\;value}{-ve\;value}$

Finally, $s = positive\;value$.

So option (C) is incorrect.

Now the final option (D) if we have displacement, velocity and acceleration for a given point of time then we can calculate the displacement for any point of time in future by using Newton’s equation of motion.

So option (D) is correct.

Therefore, Option (B) and (D) is correct.

Note:
Distance cannot be negative and thus the third option (C) is totally incorrect. Then, displacement is a fundamental quantity of motion and velocity and acceleration are its derivatives. Thus, (D) is also incorrect.