Question

When a train is stoped by applying break it stops after travelling a distance of 50 metres. If speed of train is doubled and same retarding force is applied then it stops after travelling a distance of :-
(1) 50 m
(2) 100 m
(3) 200 m
(4) 400 m​

Answer 1

Answer:

(3) 200 m

Explanation:

given that,

a train is stoped by applying break it stops after travelling a distance of 50 metres.

so,

here final velocity = 0  [train stops]

let initial velocity of train be u

distance travelled after applying brakes = 50 m

in 1st case,

we have ,

initial velocity = u

final velocity(v) = 0

distance(s) = 50 m

by the equation of motion,

v² = u² + 2as

where,

a = retardation produced by brakes

now,

putting the values,

(0)² = u² + 2a(50)

u² + 100a = 0

u² = -100a  ....(1)

2nd case...

now given that,

speed of train is doubled and same retarding force is applied

so,

now,

initial velocity = 2u

final velocity = 0

let the distance covered by the train after applying brakes in 2nd case be S

by the equation of motion

v² = u² + 2as

putting the values,

(0)² = (2u)² + 2as

2as + 4u² = 0

4u² = -2as

2u² = -as  ....(2)

now,

from eqn (1) u² = -100a

putting the values of u² on (2)

2u² = -as

2(-100a) = -as

-200a = -as

-as = -200a

-s = -200

s = 200

so,

If speed of train is doubled and same retarding force is applied then it stops after travelling a distance of

200 m

so,

Answer is option (3) 200 m

Answer 2

$\huge\boxed{Answer:-}$

Note •°•

u=initial velocity

V= 0

50 m is the distance

initial velocity = 2u

velocity final = 0

v² = u² + 2as

Adding the the values:-

(0)² = u² + 2a(50)

u² + 100a = 0

u² = -100a  Equation (1)

v² = u² + 2as

Adding the values :-

(0)² = (2u)² + 2as

2as + 4u² = 0

4u² = -2as

2u² = -as  Equation (2)

Equation(1) u² = -100a

Adding the values of u² on Equation (2)

2u² = -as

2(-100a) = -as

-200a = -as

-as = -200a

-s = -200

$\boxed{Answer:-(-s= 200)}$

Hope it helps:)

from the question :-

• Therefore, If speed of train is doubled and same retarding force is applied then it stops after travelling a distance of 200m