Lecture 1: Position, path length and displacement ; Average velocity and average speed ; Instantaneous velocity and speed

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.

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?

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

Define J = v + at from velocity time graph.

Write the characteristics of displacement?