Question

A body is moving with a velocity
1 m/s and a force F is needed to stop
it within a certain distance. If the
speed of the body becomes three
times, the force needed to stop it
within the same distance would be
(RRB JE 2008)
(a) 1.5 F (b) 3.0 F (c) 6.0 F (d) 9.0 F
​

Answer 1

Answer:

9.0 F

Explanation:

Question says that

" same displacement "

But we know ,

Force = mass × acceleration .

Let mass of body = m

Try to find displacement in F term .

Case 1 :-

initial speed = 1 m/sec

final speed = 0

F = ma

a = - F/m ( regarding )

use kinematics equation ,

v² = u² +2as

0 = 1² -2×F/mx

x = m/2F --------(1)

case 2 :-

Here we have require Force .

initial speed = 3 m/sec

final speed = 0

S = x = m/2F { same distance }

use kinematics equation ,

v² = u² +2aS

0 = 9² + 2a × m/2F

a = - 9F/m { regarding }

so, Force = mass × acceleration

= m × -9F/m

= -9F

hence, force required to stop = 9F