What is the condition for an object to be considered as a point object?

Does the displacement of an object depend on the choice of the postion of origin of the coordinate system?

For which condition, the distance and the magnitude of displacement of an object have the same values?

The displacement-time graph for two particles X and Y are straight lines making angles of 30^o and 60^o with the time axis. What is the ratio of the velocities of Y and X ?

With zero speed a particle may have non-zero velocity. Is the statement true or false, explain?

Constant acceleration menas that x - t graph will have constant slope? Yes / No

Find the acceleration  and velocity of a ball at the instant it reaches its highest point it was thrown up with velocity v.

Draw position-time graph for a body at rest.

A car starts accelerating from rest for sometime, maintains the velocity for sometime and then comes to rest with uniform deceleration. Draw v-t graph.

Suppose two trains A and B are moving with uniform velocities along parallel tracks in the same direction and the velocities of A and B be 60 km/h in East and 65 km/h in East. Find the relative velocity of B w.r.t. A.

For what condiion, an object could be considered as a point object? Describe in brief

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.

Thye position x of a body is given by x = A sin(wt). Find the time at which the displacements is maximum.

The distance travelled by a body is proportional  to the square of time. What type of motion this body has?

A car accelerates from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) to come to rest. If t is total time elapsed, then calculate
(i) the maximum velocity attained by the car
(ii) the total distance travelled by the car

The speed-time graph for a car is shown in figure below.

(i) Find how far the car travels in the first 4 s? Shade the area on the graph that represents the distance travelled by the car during the period.
(ii) Which part of the graph represent uniform motion of the car?

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).

A passenger is standing d metres away from a bus. The bus begins to move with constant acceleration (a).To catch the bus, the passanger runs at a constant speed(v) towards the bus.What must be the minimum speed of the passenger so that he may catch the bus?

The position of an object moving along x-axis is given by x = a + bt², where a = 8.5 m, b = 2.5 m s^–2 and t is measured in seconds. What is its velocity at t = 0 s and t = 2.0 s. What is the average velocity between t = 2.0 s and t = 4.0 s ?

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 car moving with a speed of 50 km/h can be stopped by brakes after at least 6m.What will be the minimum stopping distance, if the same car is moving at a speed of 100 km/h?

A jet plane beginning  its take off moves down the runway at a constant acceleration of 4.00 m/s² If a speed of 70.0 m/s is required for the plane to leave the ground, how long a runwasy is required? Because the acceleration  is constant , we can apply the equations of motion derived above.

In which of the following examples of motion, can be the body be considered approximately a point object?
A monkey sitting on the top of a man cycling smoothly on a circular track.

Uniform Acceleration
The displacement x of a particle varies with time t as \(x={ 4t }^{ 2 }-15t+25\)
Can we call the motion of the particle as one with uniform acceleration?

Two parallel rail tracks run North-South.Train A moves North with a speed of 54 kmh^-1. and train B moves South with a speed of 90 kmh^-1 . What is the velocity of monkey on the roof of the train A against its motion (with a velocity of 18 kmh^-1 with respect to train A) as observed by a man standing on the ground?