Motion in a Straight Line

A particle is moving along \(x\)-axis with its position (x) varying with time (t) as \(x=\alpha {t}^{4}+\beta {t}^{2}+\gamma t+\delta\). The ratio of its initial velocity to its initial acceleration, respectively, is:

A particle is moving along \(x\)-axis with its position (x) varying with time (t) as \(x=\alpha {t}^{4}+\beta {t}^{2}+\gamma t+\delta\). The ratio of its initial velocity to its initial acceleration, respectively, is:

In some appropriate units, time \(t\) and position \(x\) relation of a moving particle is given by \(t={x}^{2}+x\). The acceleration of the particle is;

[NEET 2025]

When a ruler falls vertically, 5 different persons catch it with different reaction times. (g = 9.8 ms^–2)

A. Person A has reaction time of 0.20 s.
B. Person B has reaction time of 0.22 s.
C. Person C has reaction time of 0.18 s.
D. Person D has reaction time of 0.19 s.
E. Person E has reaction time of 0.21 s.
What is the correct order of the distance travelled by the ruler for each person ?

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is :

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of \(60\mathrm{km}/\mathrm{h}\) in the direction X to Y notices that a bus goes past her every \(30\) minutes in the direction of her motion, and every \(10\) minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

Train A and train B are running on parallel tracks in opposite directions with speeds of 36km/hour and 72 km/hour, respectively, A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km / hour. Speed (in \(m{s}^{-1}\)) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

An engine of a train, moving with uniform acceleration, passes the signal - post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is :

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

[JEE Main 2023, 12 Apr (Shift 1)]

A balloon was moving upwards with a uniform velocity of \(10 \ m / s\). An object of finite mass is dropped from the balloon when it was at a height of \(75 \ m\) from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of \(g\) as \(\left.10 \ m / s ^2\right)\)

[JEE Main 2021, 25 Jul (Shift 2)]

Given below are two statements:
Statement-I: Area of the 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 person sitting in the ground floor of a building notices through the window, of height \( 1.5 \mathrm{~m} \), a ball dropped from the roof of the building crosses the window in \( 0.1 \mathrm{~s} \). What is the velocity of the ball when it is at the topmost point of the window? \( \left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right) \)