Motion in a Straight Line Physics - Motion in a Straight Line

The variation of quantity A with quantity B, plotted in Fig. describes the motion of a particle in a straight line.

1. Quantity B may represent time.
2. Quantity A is velocity if motion is uniform.
3. Quantity A is displacement if motion is uniform.
4. Quantity A is velocity if motion is uniformly accelerated.

Among the four graphs Fig. there is only one graph for which average velocity over the time intervel (0, T ) can vanish for a suitably chosen T. Which one is it?

A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?

1. x < 0, v < 0, a > 0.
2. x > 0, v < 0, a < 0.
3. x > 0, v < 0, a > 0.
4. x > 0, v > 0, a < 0.

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
Rate of change of momentum is force. Estimate how much force such a drop would exert on you.

A monkey climbs up a slippery pole for 3 seconds and subsequently slips for 3 seconds. Its velocity at time t is given by v(t) = 2t(3 - t); 0 < t < 3 and v(t) = -(t - 3)(6 - t) for 3 < t < 6s in m/s. It repeats this cycle till it reaches the height of 20m.
At what time is its acceleration maximum in magnitude?

A man is standing on top of a building 100m high. He throws two balls vertically, one at t = 0 and other after a time interval (less than 2 seconds). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is +15m at t = 2s. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throw.

A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of 18m/h while the other has the speed of 27km/h. The bird starts moving from first car towards the other and is moving with the speed of 36km/h and when the two cars were separted by 36km. What is the total distance covered by the bird? What is the total displacement of the bird?

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
Estimate the time required to flatten the drop.

A monkey climbs up a slippery pole for 3 seconds and subsequently slips for 3 seconds. Its velocity at time t is given by v(t) = 2t(3 - t); 0 < t < 3 and v(t) = -(t - 3)(6 - t) for 3 < t < 6s in m/s. It repeats this cycle till it reaches the height of 20m.
At what time is its average velocity maximum?

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.

A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.

A monkey climbs up a slippery pole for 3 seconds and subsequently slips for 3 seconds. Its velocity at time t is given by v(t) = 2t(3 - t); 0 < t < 3 and v(t) = -(t - 3)(6 - t) for 3 < t < 6s in m/s. It repeats this cycle till it reaches the height of 20m.
At what time is its velocity maximum?

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. (g = 10m/s²)

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time. (Take acceleration in the backward direction as positive).

A monkey climbs up a slippery pole for 3 seconds and subsequently slips for 3 seconds. Its velocity at time t is given by v(t) = 2t(3 - t); 0 < t < 3 and v(t) = -(t - 3)(6 - t) for 3 < t < 6s in m/s. It repeats this cycle till it reaches the height of 20m.
How many cycles (counting fractions) are required to reach the top?

Give examples of a one-dimensional motion where:
The particle moving along positive x-direction comes to rest periodically and moves forward.

Refer to the graphs in Fig. Match the following.

Graph		Characteristic
a.	i.	has v > 0 and a < 0 throughout.
b.	ii.	has x > 0 throughout and has a point with v = 0 and a point with a = 0.
c.	iii.	has a point with zero displacement for t > 0.
d.	iv.	has v < 0 and a > 0.

A man runs across the roof-top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is of a lower height than the first. If his speed is 9m/s, the (horizontal) distance between the two buildings is 10m and the height difference is 9m, will he be able to land on the next building? (take g = 10m/s²).

A ball is dropped and its displacement vs time graph is as shown Fig. (displacement x is from ground and all quantities are +ve upwards).

1. Plot qualitatively velocity vs time graph.
2. Plot qualitatively acceleration vs time graph.

A ball is dropped from a building of height 45m. Simultaneously another ball is thrown up with a speed 40m/s. Calculate the relative speed of the balls as a function of time.

An object falling through a fluid is observed to have acceleration given by a = g - bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?