Motion in a Straight Line

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