Q: A passenger sitting in a train A moving at 90 ~km / h observes another train B moving in the opposite direction for 8 ~s . If the velocity of the train B is 54 ~km / h , then length of train B is :

Velocity of train A $ V _ A =90 km hr =90 5 18 =25 ~m / s $ Velocity of train B $ V _ B =54 km hr =54 5 18 =15 ~m / s $ Velocity of train B w.r.t. train $ aligned A= V _B & - V _A \\ & =15-(-25) m / s \\ & =40 ~m / s aligned $ Time of crossing $= length of train relative velocity $ $(8)= 40 $ $ =8 40=320$ meter.

Question 1

A particle is moving in a straight line. The variation of position ' x ' as a function of time ' t ' is given as x= (t^3-6 t^2+20 t+15 ) m. The velocity of the body when its acceleration becomes zero

Accepted Answer

Displacement, x=t^3-6 t^2+20 t+15 Velocity, v= dx dt =3 t ^2-12 t +20 Acceleration, a= d v d t =6 t-12 When a=0 6 t -12=0 t=2 ~s At t =2 ~s , v=3(2)^2-12(2)+20=8 ~m / s

Question 2

The distance travelled by a particle starting from rest and moving with an acceleration 4 3 ~ms ^ -2 , in the third second is:

Accepted Answer

Distance travelled in the nth second is given by t _ n = u + a 2 (2 n -1) put u =0, a = 4 3 ~ms ^ -2 , n =3 d=0+ 4 3 2 (2 3-1)= 4 6 5= 10 3 m

Question 3

A passenger sitting in a train A moving at 90 ~km / h observes another train B moving in the opposite direction for 8 ~s . If the velocity of the train B is 54 ~km / h , then length of train B is :

Accepted Answer

Velocity of train A $ V _ A =90 km hr =90 5 18 =25 ~m / s $ Velocity of train B $ V _ B =54 km hr =54 5 18 =15 ~m / s $ Velocity of train B w.r.t. train $ aligned A= V _B & - V _A \ & =15-(-25) m / s \ & =40 ~m / s aligned $ Time of crossing $= length of train relative velocity $ $(8)= 40 $ $ =8 40=320$ meter.

Question 4

An object moves with speed v_1, v_2 and v_3 along a line segment A B, B C and C D respectively as shown in figure. Where A B=B C and A D=3 A B, then average speed of the object will be:

Accepted Answer

Consider, AB =x BC =x 2 x+ CD =3 x CD =3 x-2 x=x Average speed of the object = Total distance Total time = 3 x x v_1 + x v_2 + x v_3 = 3 v_1 v_2 v_3 v_2 v_3+v_1 v_3+v_1 v_2

Question 5

A balloon is rising vertically up with a velocity of 29 ~ms ^ -1 . A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was

Accepted Answer

For stone to be dropped from rising balloon of velocity 29 ~m / s , u =-29 ~m / s , t =10 sec . array l h =-29 10+ 1 2 9.8 100 \ =-290+490=200 ~m . array

Motion In One Dimension — Previous Year Questions & Solutions