Motion in a Straight Line · Question 4

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

1. 10 min, 90 km/h
2. 15 min, 120 km/h
3. 9 min, 40 km/h
4. 25 min, 100 km/h

The velocity (v)- time (t) plot of the motion of a body is shown below: [figure] The acceleration (a)- time (t) graph that best suits this motion is :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A particle is moving along x-axis with its position (x) varying with time (t) as x = t4 + t2 + t + . The ratio of its initial velocity to its initial acceleration, respectively, is:

1. 2 :
2. : 2
3. 4 :
4. : 2

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is :

1. 2v3
2. 4v3
3. 3v4
4. v3

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s-1. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s-2)

1. 60 m
2. 64 m
3. 68 m
4. 56 m

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u3. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

1. 24 cm
2. 28 cm
3. 30 cm
4. 27 cm

The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second

1. 1 : 2 : 3 : 4
2. 1 : 4 : 9 : 16
3. 1 : 3 : 5 : 7
4. 1 : 1 : 1 : 1

The displacement-time graphs of two moving particles make angles of 30 and 45 with the x-axis as shown in the figure. The ratio of their respective velocity is [figure]

1. 3 : 1
2. 1 : 1
3. 1 : 2
4. 1 : 3

The position-time (x - t) graph for positive acceleration is

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sn be the distance travelled by the block in the interval t = n - 1 to t = n. Then the ratio SnSn+1 is :

1. 2n2n-1
2. 2n-12n
3. 2n-12n+1
4. 2n+12n-1