Chapter 3 - MOTION IN A STRAIGHT LINE

A man is standing on top of a building 100 m 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 +15 m at
t = 2 s. 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 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 < 6 s in
m/s. It repeats this cycle till it reaches the height of 20 m.
(a) At what time is its velocity maximum?
(b) At what time is its average velocity maximum?
(c) At what time is its acceleration maximum in magnitude?
(d) How many cycles (counting fractions) are required to reach the
top?

A motor car moving at a speed of 72km/h can not come to a stop
in less than 3.0 s while for a truck this time interval is 5.0 s. On a
higway the car is behind the truck both moving at 72km/h. The
truck gives a signal that it is going to stop at emergency. At what
distance the car should be from the truck so that it does not bump
onto (collide with) the truck. Human response time is 0.5s.

It is a common observation that rain clouds can be at about a
kilometre altitude above the ground.
(a) 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)
(b) A typical rain drop is about 4mm diameter. Momentum is mass
x speed in magnitude. Estimate its momentum when it hits
ground.
(c) Estimate the time required to flatten the drop.
(d) Rate of change of momentum is force. Estimate how much force
such a drop would exert on you.
(e) Estimate the order of magnitude force on umbrella. Typical
lateral separation between two rain drops is 5 cm.
(Assume that umbrella is circular and has a diameter of 1m
and cloth is not pierced through !!)

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

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 9
m/s, the (horizontal) distance between the two buildings is 10 m
and the height difference is 9 m, will he be able to land on the next
building?

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 18
m/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 36 km.
What is the total distance covered by the bird? What is the total
displacement of the bird?

Define (i) v = u + at (ii) V² – u² = 2as by calculus method

Define (i) v = u + at (ii) V² – u² = 2as by calculus method

(a) Define the term relative velocity?
(b) Write the expression for relative velocity of one moving with respect to
another body when objects are moving in same direction and are moving in
opposite directions?
(c) A Jet airplane traveling at the speed of 500km/hr ejects its products of
combustion at the speed of 1500km/h relative to the Jet plane. What is the
speed of the latter with respect to an observer on the ground?

A car moving on a straight highway with speed of 126km/hr. is brought to stop
within a distance of 200m. What is the retardation of the car (assumed uniform)
and how long does it take for the car to stop?

A balloon is ascending at the rate of 4.9m/s. A pocket is dropped from the balloon
when situated at a height of 245m. How long does it take the packet to reach the
ground? What is its final velocity?

The displacement x of a particle moving in one dimension under the action of
constant force is related to the time by the equation where x is in meters and t is in
seconds. Find the velocity of the particle at (1) t = 3s (2) t = 6s.

Draw displacement time graph for a uniformly accelerated motion? What is its
shape?

What is the shape of the displacement time graph for uniform linear motion?

Under what condition the displacement and the distance of a moving object
will have the same magnitude?

A stone is dropped from the top of a cliff and is found to ravel 44.1m diving the last

second before it reaches the ground. What is the height of the cliff? g = 9.8m/s²

Establish the relation Snth = u + a/2(2n -1) where the letters have their usual
meanings.

A police jeep on a petrol duty on national highway was moving with a speed of
54km/hr. in the same direction. It finds a thief rushing up in a car at a rate of
126km/hr in the same direction. Police sub – inspector fired at the car of the thief
with his service revolver with a muzzle speed of 100m/s. with what speed will the
bullet hit the car of thief?

A particle is thrown upwards. It attains a height (h) after 5 seconds and again after
9s comes back. What is the speed of the particle at a height h?

Displacement of a particle is given by the expression x = 3t² + 7t – 9, where x is in

meter and t is in seconds. What is acceleration?

What causes variation in velocity of a particle?

Can speed of an object be negative? Justify

Shipra went from her home to school 2.5km away. On finding her home closed she
returned to her home immediately. What is her net displacement? What is the total
distance covered by her?

A railway train 400m long is going from New Delhi railway station to Kanpur.
Can we consider railway train as a point object

A particle is moving along a straight line and its position is given by the relation

x = (t³ - 6t ² -15t + 40)m

Find (a) The time at which velocity is zero.

(b) Position and displacement of the particle at that point.

(c) Acceleration for the particle at that line.

Define J = v + at from velocity time graph.

Sameer went on his bike from Delhi to Gurgaon at a speed of 60km/hr and came
back at a speed of 40km/hr. what is his average speed for entire journey.

Draw displacement time graph for uniformly accelerated motion. What is its
shape?

Write the characteristics of displacement?

What is the relative velocity of two bodies having equal velocities?

Two balls of different masses are thrown vertically upward with same initial speed.
Which one will rise to a greater height?

Under what condition is the relation s =ut correct?

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h^-1. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h^-1. What is the
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min ? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !]

Explain clearly, with examples, the distinction between:
(a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.
When is the equality sign true? [For simplicity, consider one-dimensional motion only].

A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Read each statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion
(a) with zero speed at an instant may have non-zero acceleration at that instant
(b) with zero speed may have non-zero velocity,
(c) with constant speed must have zero acceleration,
(d) with positive value of acceleration mustbe speeding up.

A player throws a ball upwards with an initial speed of 29.4 m s^-1.
(a) What is the direction of acceleration during the upward motion of the ball ?
(b) What are the velocity and acceleration of the ball at the highest point of its motion ?
(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.
(d) To what height does the ball rise and after how long does the ball return to the player’s hands ? (Take g = 9.8 m s^-2 and neglect air resistance).

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h^-1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

On a two-lane road, car A is travelling with a speed of 36 km h^-1. Two cars B and C approach car A in opposite directions with a speed of 54 km h^-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident ?

Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^-1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s^-2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them ?

A car moving along a straight highway with speed of 126 km h^-1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?

A jet airplane travelling at the speed of 500 km h^-1 ejects its products of combustion at the speed of 1500 km h^-1 relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ?

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

A woman starts from her home at 9.00 am, walks with a speed of 5 km h^-1 on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 km h^-1. Choose suitable scales and plot the x-t graph of her motion.

 In which of the following examples of motion, can the body be considered approximately a point object:
(a) a railway carriage moving without jerks between two stations.
(b) a monkey sitting on top of a man cycling smoothly on a circular track.
(c) a spinning cricket ball that turns sharply on hitting the ground.
(d) a tumbling beaker that has slipped off the edge of a table.