Question

a body of mass 2 kg moving on a horizontal surface with initial velocity of 4 metre per second comes to rest after two seconds if one wants to keep this body moving on the same surface with a velocity of 4 metre per second the force required is

Answer 1

Answer:

Explanation:

Mass (m) = 2kg (Given)

Initial velocity (u) = 4m/s (Given)

If there is no change in velocity then u = v , then mv - mv = 0, whereas when there is a change -

Using first equation of motion - a = v-u/t

= 0-4/2

= -4/2

= -2

Force required to keep the body in same velocity is F = m x a 

Change in velocity means acceleration - 

F = m x a 

F = 2 x 2

 F = 4 N 

Thus, according to Newton's first law of motion the body will continue to be straight motion or in a state of rest until an external force is applied on it , in this case a force of 4n is required to keep body moving with same velocity.

Answer 2

Answer:  

The force required by the body is 4N.

Solution:

The given data’s are  

Mass of the body m = 2 kg

Initial velocity u = 4 m/s

Final Velocity v = 0

Time taken to stop t = 2 s.

As the body was moving initially and then it came to rest that means the body undergoes deceleration or negative acceleration. Acceleration is the rate of ‘change of velocity’ with time. So, the deceleration can be obtained as  

$\text {acceleration} =\frac{\text {final velocity -initial velocity}}{\text {time}}$

$\text {acceleration}=\frac{4-0}{2}=2\ \mathrm{m} / \mathrm{s}^{2}$

According to Newton’s second law, the force is directly proportional to the ‘mass of the body’ and acceleration exerted by the body. So if we have to keep the body moving with the initial velocity, the body should retain the force it exerted before stopping of the body.

Thus,

$\text {Force}=\text {Mass} \times \text {Acceleration}$

$\bold{\text {Force}=2 \times 2=4 N}$

So, the body require a force of 4N to keep it moving.