Motion in a Straight Line

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