Motion in a Straight Line

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is m. (Take g=10 m/s2)

1. 85
2. 150
3. 129
4. 125

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5th second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is x8. The value of x is .

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is m. (Take g=10 m/s2 and neglect the air resistance)

The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively . [figure]

1. 25 m and zero
2. 50 m and zero
3. 100 m and zero
4. 100 m and 2.5 m/s

Two cars A and B are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car A is moving ahead of car B. A person in car B throws a stone with a speed v so that it hits the car A with a speed of 5 m/s. The value of v is km/h.

1. 18
2. 28
3. 38
4. 48

A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?

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

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is m. (g = 10 m/s2)

1. 3.8
2. 4.0
3. 4.2
4. 2.5

A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t3 - 3t Choose the correct answer from the options given below :

1. A, C, D Only
2. A, B, C Only
3. C, E Only
4. A, C Only

The velocity (v) – distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system? [figure]

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

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with 3 m/s2. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is m. (g = 10 m/s2)

1. 92.5
2. 62.5
3. 20
4. 82.5

The displacement x versus time graph is shown below. [figure] Choose the correct answer from the options given below :

1. (B), (C), (D) only
2. (B), (D), (E) only
3. (A), (D), (E) only
4. (B), (C), (E) only

Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below :

1. A, B and C only
2. A, C and D only
3. A, B and D only
4. A and B only

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x = c0 (t2 - 2 ) + c(t - 2)2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. the acceleration of the particle is 2(c + c0)
2. the acceleration of the particle is 2c0
3. the acceleration of the particle is 2c
4. the initial velocity of the particle is 4c

A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next 32x distance. The average velocity in this motion is 507 m/s. If v1 is 5 m/s then v2 = m/s.

A sportsman runs around a circular track of radius r such that he traverses the path ABAB. The distance travelled and displacement, respectively, are [figure]

1. r, 3r
2. 2r, 3 r
3. 3 r, 2r
4. 3 r, r

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is .

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4 s? [figure]

1. 11 m
2. 30 m
3. 13 m
4. 10 m

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is km . [figure]

1. 12
2. 6
3. 3
4. 9