Question

a body is moving with a velocity of 1 m/s . if the force F is needed to stop it within the distance x . if the speed of the body is 3 m/s ,then the force needed to stop it within the same distance x will be:

a. 1.5 F b. 3 F c. 6 F d, 9 F

Answer 1

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

Answer 2

ANS.

RIGHT ANSWER IS 9F.