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A body of mass 'm' is travelling with a velocity `u'. When a constant retarding force 'F' is applied, it comes to rest after travelling a distance `s1'. If the initial velocity is '2u', with the same force 'F', the distance travelled before it comes to rest is `s2'. Then 

A body of mass 'm' is travelling with a velocity `u'. When a constant retarding force 'F' is applied, it comes to rest after travelling a distance `s1'. If the initial velocity is '2u', with the same force 'F', the distance travelled before it comes to rest is `s2'. Then  Correct Answer s<sub>2</sub> = 4s<sub>1</sub>

CONCEPT:

  • When a body moves in a straight line under constant acceleration, it follows three equations of motion.

All unknowns are found by these equations.

  1. v = u + at;
  2. s = ut + (1/2) at2 
  3. v2 = u2 + 2as

Where u is initial velocity, v is final velocity, a is constant acceleration, t is time and s is displacement.

  • Newton's second law: When a constant force acts on a body, it causes it to accelerate.

The acceleration of the body is calculated by:

F = ma

where F is the force on the body, m is the mass of the body, and a is the acceleration.

CALCULATION:

In both the cases applied force on the body is F so by Newton's Second Law, acceleration

a = F/m (constant)

The acceleration will be negative because it is decreasing the velocity.

From 3rd equation of motion

v2 = u2 + 2as

  • in first case initial velocity = u, final velocity = 0 (at rest), distance travelled is s1

02 = u2 + 2(-a)s1

s1 = u2/2a

  • in first case initial velocity = 2u, final velocity = 0 (at rest), distance travelled is s1

02 = (2u)2 + 2(-a)s2

s2 = 4u2/2a

s2 = 4 s1 

So the correct answer is option 4.

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