The displacement x of a particle varies with time according to the relation x=\(\frac { a }{ b } \)(1-e^-bt). Then

The displacement of an object at any instant is given by x = 30 + 20 t², where x is in metres and t in seconds. The acceleration of the object will be

The area under the velocity time graph between any two instants t = t₁ and t = t₂ gives the distance covered in a time \(\delta \) t = t₂ - t₁.

Which of the following is not a vector quantity?

When the distance travelled by a body is directly proportional to the time, the body is said to have a

Identify one dimensional motion out of the following:

A bus starting from rest moves with a uniform acceleration of 0.1 m / s² for 2 min. Find the
(i) the speed acquired
(ii) the distance travelled.

What is meant by 'point object' in physics?

Can a particle have acceleration at an instant if its velocity is zero at that instant? Give example.

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

Explain the difference between uniform velocity and variable velocity.

To what height does the ball rise and after how long does the ball return to the player's hands?(Take g = 9.8ms^-2 and neglect air resistance)

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 must be speeding up.

A certain automobile manufacturer claims that its super-delux sports car will accelerate from rest to a speed of 42.0 ms:' in 8.0 s. Under the important assumption that the acceleration is constant,
(a) Determine the acceleration of car in ms^-2.
(b) Find the distance the car travels in 8.0 s.
(c) Find the distance the car travels in 8^th second.

The velocity of a particle is given by equation v = 4 + 2 (c₁ + c₂ t), where c₁and c₂ are constant. Find the initial velocity and acceleration of the particle.

Establish the kinematic equation v² - u² = 2as from velocity-time graph for a uniformly accelerated motion.

Paul went to Shimla with his friends on a college trip. In Shimla, they went for ride in a hot air balloon. They were in picnic mood, so they took different variety of food packets with them. As the balloon rose up and started wandering in the air they started enjoying. Suddenly, Paul saw that at a place some people were struck on an island and shouting for help. He wanted to help those people but all be could do at that time was dropping the food packets so that they could survive till the help arrived after coming down on the ground, he immediately called the police to help those people.
(iii) What will be the position-time curve for dropped packet?

(i) Draw position-time graph for
(a) Accelerated motion  
(b) Retarded motion
(ii) A juggler throws balls into air. He throws one whenever the previous one is at its highest point.How high do the balls rise if he throws n balls in each second? Take acceleration due to gravity as g.

A juggler throws balls into air. He throws one whenever the previous one is at its highest point.How high do the balls rise if he throws n balls in each second? Take acceleration due to gravity as g.