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The velocity of a particle is \( v = v_0 + g t + F t^2 \). Its position is \( x = 0 \) at \( t = 0 \); then its displacement after time \( (t = 1) \) is:

Water drops are falling from a nozzle of a shower onto the floor, from a height of \( 9.8 \, \text{m} \). The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

A balloon was moving upwards with a uniform velocity of \( 10 \, \text{m/s} \). An object of finite mass is dropped from the balloon when it was at a height of \( 75 \, \text{m} \) 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 \( 10 \, \text{m/s}^2 \))

A mosquito is moving with a velocity \( \vec{v} = 0.5 \, t^{2} \, \hat{i} + 3 t \, \hat{j} + 9 \hat{k} \, \text{m/s} \) and accelerating in uniform conditions. What will be the direction of mosquito after \( 2 \, \text{s} \)?

Two spherical balls having equal masses with radius of \( 5 \, \text{cm} \) each are thrown upwards along the same vertical direction at an interval of \( 3 \, \text{s} \) with the same initial velocity of \( 35 \, \text{m /s}^{} \), then these balls collide at a height of _________ \( \text{m} \). (take \( g = 10 \, \text{m /s}^{2} \))

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

1.A swimmer wants to cross a river from point A to point B. Line AB makes an angle of \( 30^\circ \) with flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \( \theta \) with the line AB should be ______\( ^\circ \), so that the swimmer reaches point B.

A ball is thrown up with a certain velocity so that it reaches a height '\( h \)'. Find the ratio of the two different times of the ball reaching \( \dfrac{h}{3} \) in both the directions.

The velocity-displacement graph of a particle is shown in the figure.

The acceleration-displacement graph of the same particle is represented by:

A car accelerates from rest at a constant rate \( \alpha \) for some time after which it decelerates at a constant rate \( \beta \) to come rest. If the total time elapsed is \( t \) seconds, the total distance travelled is:

A butterfly is flying with a velocity \( 4\sqrt{2} \, \text{m/s} \) in North-East direction. Wind is slowly blowing at \( 1 \, \text{m/s} \) from North to South. The resultant displacement of the butterfly in \( 3 \) second is:

The instantaneous velocity of a particle moving in a straight line is given as \( v = \alpha t + \beta t^{2} \), where \( \alpha \) and \( \beta \) are constants. The distance travelled by the particle between \( 1 \, \text{s} \) and \( 2 \, \text{s} \) is:

A rubber ball is released from a height of \( 5 \, \text{m} \) above the floor. It bounces back repeatedly, always rising to \( \dfrac{81}{100} \) of the height through which it falls. Find the average speed of the ball. (Take \( g = 10 \, \text{m s}^{-2} \))

A body of mass \( 2 \, \text{kg} \) moves under a force of \( (2\hat{i} + 3\hat{j} + 5\hat{k} )\, \text{N} \). It starts from rest and was at the origin initially. After \( 4 \, \text{s} \), its new coordinates are \( (8, b, 20) \). The value of \( b \) is ______. (Round off to the Nearest Integer)

The relation between time \( t \) and distance \( x \) for a moving body is given as \( t = m x^2 + n x \), where \( m \) and \( n \) are constants. The retardation of the motion is: (Where \( v \) stands for velocity)

A force \( \vec{F} = (40\hat{i} + 10\hat{j}) \, \text{N} \) acts on a body of mass \( 5 \, \text{kg} \). If the body starts from rest, its position vector \( \vec{r} \) at time \( t = 10 \, \text{s} \), will be:

A particle is moving with constant acceleration ‘\( a \)’. Following graph shows \( v^2 \) versus \( x \) (displacement) plot. The acceleration of the particle is ______ \( \mathrm{m/s^2} \).

A player kicks a football with an initial speed of \( 25 \, \text{ms}^{-1} \) at an angle of \( 45^\circ \) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion?
(Take : \( g = 10 \, \text{ms}^{-2} \))

If the velocity of a body related to displacement \( x \) given by \( v=\sqrt{5000+24x} \, \mathrm{m/s} \), then the acceleration of the body is __________ \( \mathrm{m/s^2} \).

Water droplets are coming from an open tap at a particular rate, The spacing between a droplet observed at \( 4^{\text{th}} \) second after its fall to the next droplet is \( 34.3 \ \text{m} \). At what rate the droplets are coming from the tap? (Take \( g=9.8 \ \text{m}/\text{s}^{2} \))

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JEE Main 2021 17th March Morning Shift

A car accelerates from rest at a constant rate \( \alpha \) for some time after which it decelerates at a constant rate \( \beta \) to come rest. If the total time elapsed is \( t \) seconds, the total distance travelled is: