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A particle starts with an initial velocity of \( 10.0 \, \text{ms}^{-1} \) along \( x \)-direction and accelerates uniformly at the rate of \( 2.0 \, \text{ms}^{-2} \). The time taken by the particle to reach the velocity of \( 60.0 \, \text{ms}^{-1} \) is _________.

To maintain a speed of \( 80 \, \text{km/h} \) by a bus of mass \( 500 \, \text{kg} \) on a plane rough road for \( 4 \, \text{km} \) distance, the work done by the engine of the bus will be _____ \( \text{KJ} \). (The coefficient of friction between tyre of bus and road is \( 0.04 \).)

The position-time graphs for two students A and B returning from the school to their homes are shown in figure:

(A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travles faster than B (E) B travel faster than A
Choose the correct answer from the options given below:

Given below are two statements:
Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance.
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer from the options given below

Given below are two statements:
Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration- time graph is equal to the change in velocity-in the given time.
In the light of given statements, choose the correct answer from the options given below:

A car travels a distance of \( 'x' \) with speed \( v_{1} \) and then same distance \( 'x' \) with speed \( v_{2} \) in the same direction. The average speed of the car is:

A vehicle travels \( 4 \, \text{km} \) with speed of \( 3 \, \text{km/h} \) and another \( 4 \, \text{km} \) with speed of \( 5 \, \text{km/h} \), then its average speed is :

A horse rider covers half the distance with \(5 \, \text{m/s}\) speed. The remaining part of the distance was travelled with speed \(10 \, \text{m/s}\) for half the time and with \(15 \, \text{m/s}\) for other half of the time. The mean speed of the rider averaged over the whole time of motion is \( \frac{x}{7} \, \text{m/s} \). The value of \( x \) is _______.

The distance travelled by an object in time \( t \) is given by \( s = (2.5)t^{2} \). The instantaneous speed of the object at \( t = 5 \, \text{s} \) will be:

Match Column-I with Column-II.

Choose the correct answer from the options given below:

The distance travelled by a particle is related to time \( t \) as \( x = 4 t^2 \). The velocity of the particle at \( t = 5 \, \text{s} \) is:

The position of a particle related to time is given by \( x = (5t^2 - 4t + 5) \, \text{m} \). The magnitude of velocity of the particle at \( t = 2 \, \text{s} \) will be:

A projectile is projected at \( 30^\circ \) from horizontal with initial velocity \( 40 \, \text{m} \, \text{s}^{-1} \). The velocity of the projectile at \( t = 2 \, \text{s} \) from the start will be:

The velocity time graph of a body moving in a straight line is shown in figure.

The ratio of displacement to distance travelled by the body in time \( 0 \) to \( 10 \, \text{s} \) is:

A particle of mass \( 10 \, \text{g} \) moves in a straight line with retardation \( 2x \), where \( x \) is the displacement in SI units. Its loss of kinetic energy for above displacement is \( \left( \dfrac{10}{x} \right)^{-n} \, \text{J} \). The value of \( n \) will be _________.

An object moves with speed \( v_{1} \), \( v_{2} \) and \( v_{3} \) along a line segment \( AB \), \( BC \) and \( CD \) respectively as shown in figure. Where \( AB = BC \) and \( AD = 3AB \), then average speed of the object will be:

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object its velocity is \( -4\hat{j}\ \text{m/s} \). The object’s velocity \( (v) \) and acceleration \( (A) \) at \( x = -2\ \text{m} \) will be:

A car is moving on a circular path of radius \( 600\,\text{m} \) such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of \( 54\,\text{km/hr} \) \( t(1-e^{-\pi/2})\,\text{s} \). The value of \( t \) is __________.

A ball is thrown vertically upward with an initial velocity of \( 150 \, \text{m/s} \). The ratio of velocity after \( 3 \, \text{s} \) and \( 5 \, \text{s} \) is \( \dfrac{x+1}{x} \). The value of \( x \) is_____. (take, \( g = 10 \, \text{m/s}^{2} \))

From the \( v\text{-}t \) graph shown, the ratio of distance to displacement in \( 25 \, \text{s} \) of motion is:

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JEE Main 2023 30th Jan Morning Shift

Match Column-I with Column-II.

Choose the correct answer from the options given below: