Q.A retarding force is applied to stop a train . The train stop after 80m.if the speed is doubled, then the distance travelled when same retarding force is applied is. (A) the same (B) doubled (C) halved (D) four times ?? Chose the correct option and with explain?

Question

Answer

Is it 4 times..Fretarding=m(-a).v=0,-a=V^2-u^2/2s.a=u^2/2s...Fret=mu^2/2s..here ,F is directly proportional to u^2 and inversely proportional to s...F1/F2=(u^2) s2 / (2u^2) s1.given both retarding forces are equal..then,s1/s2=u^2/4u^2.80/s2=1/4.s2=320...I.e.it is 4 times of initial..

Answer

Given

u1=u u2=2u

v1=0 v2=0

a1=-a a2=-a

s1=s1 s2=?

Now according to equation of motion

v² - u² = 2as

0 - u² = - 2as1.........(1)

0 - 4u² = - 2as2............(2) [ negative sign shows retardation]

dividing eqn (1) by eqn (2)

1/4=s1/s2

=> s2 = 4 s1

Hence the distance will be increased by 4 times.....

Answer

Answer:

To analyze the situation and determine the distance traveled when the same retarding force is applied after doubling the speed of the train, we can use the equations of motion.

Let's denote the initial speed of the train as V and the distance traveled as S. We are given that the train stops after traveling a distance of 80m, so we can write the equation of motion for the initial speed as:

V^2 = U^2 + 2as

Where U is the final velocity (0 since the train stops), a is the acceleration (retarding force/mass of the train), and s is the distance traveled (80m).

Now, let's consider the situation when the speed is doubled. The new speed of the train will be 2V, and we need to find the distance traveled, denoted as S'.

Using the same equation of motion, we can write:

(2V)^2 = U^2 + 2aS'

Since the retarding force and the mass of the train are the same in both situations, we can simplify the equation to:

4V^2 = U^2 + 2aS'

Comparing this equation with the original one, we can see that the only difference is the distance traveled. Therefore, we can conclude that the distance traveled when the speed is doubled and the same retarding force is applied is the same as the initial distance traveled.

Answer: (A) The same

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