Kinematic Equations for Uniformly Accelerated Motion

A ball is dropped from a high rise platform at, $t=0$ starting from rest. After $6 \mathrm{s}$ another ball is thrown downwards from the same platform with the speed $v$. The two balls meet at, $t=18 \mathrm{s}$. What is the value of $v$? (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

Two bodies, $\mathrm{A}$ (of mass $1 \mathrm{kg}$) and $\mathrm{B}$ (of mass $3 \mathrm{kg}$), are dropped from heights of $16 \mathrm{m}$ and $25 \mathrm{m}$, respectively. The ratio of the times taken by them to reach the ground is

A particle has initial velocity $\left(2\hat{i}+3\hat{j}\right)$ and acceleration $\left(0.3\hat{i}+0.2\hat{j}\right)$. The magnitude of velocity after $10 \mathrm{s}$ will be

A $0.4 \mathrm{kg}$ mass takes $8 \mathrm{s}$ to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is _____ $\mathrm{J}$. [Take $g=10 {\mathrm{ms}}^{-2}$]

Two body of masses $1 \mathrm{kg}$ and $2 \mathrm{kg}$ moving with same velocities are stopped by the same  force. Then the ratio of their stopping distance is

A particle is projected with velocity ${\mathrm{v}}_0$ from the ground in the vertically upward direction. The speed of the particle becomes half at height of $60 \mathrm{m}$. The value of ${\mathrm{v}}_0$, is $(\mathrm{g}=10 {\mathrm{ms}}^{-2})$ 

Determine speed $v$ acquired by block as it covers distance $6 \mathrm{m}$ starting from rest.

A body is projected from ground, vertically upwards travels a distance h in the last second of its total journey. If it is projected with twice the previous velocity, the distance travelled in last second of its journey, is 

Complete the following table.

Two cars A and B are at a position $100 \mathrm{m}$ and $200 \mathrm{m}$ from the origin at time $t=0$. They start simultaneously with velocities $10 \mathrm{m}/\mathrm{s}$ and $5 \mathrm{m}/\mathrm{s}$ respectively. Determine the position and time at which they will overtake one another. Assume they are in same direction.

A stone starts falling freely under gravity. The time taken by the stone to fall through the initial height $h$ is $4 \mathrm{s}$. The further time taken to fall through the next $2h$ height will be closest to

A train accelerating uniformly from rest attains a maximum speed of $40 {\mathrm{ms}}^{-1}$ in $20 \mathrm{s}$. It travels at this speed for$20 \mathrm{s}$ and is brought to rest with uniform retardation in further $40 \mathrm{s}$. What is the average velocity during this period?

If a body starting from the rest travels with a uniform acceleration of $10 \mathrm{m} {\mathrm{s}}^{-2}$ for first $10 \mathrm{seconds}$ and with uniform acceleration $5 \mathrm{m} {\mathrm{s}}^{-2}$ for next $20 \mathrm{seconds}$, then average acceleration of the body for $30 \mathrm{s}$ is:

A bus is running on a highway at a speed of $20 \mathrm{m}/\mathrm{s}$. A man is at a distance of $100 \mathrm{m}$ from the highway and $400 \mathrm{m}$ from the bus at an  instant. Find the minimum speed of running of man (in m/s) so that he could catch the bus.

A particle moves in a straight line with constant Velocity of $5 \mathrm{m}/\mathrm{s}$ for $2 \mathrm{s}$. It then moves with a constant acceleration of$-2 \mathrm{m}/{\mathrm{s}}^2$ for $8 \mathrm{s}$. Draw a velocity time graph for $10 \mathrm{s}$ and find final velocity and displacement and total distance?

A bullet comes out of the barrel of gun of length $23 \mathrm{m}$ with a speed $27 \mathrm{km}/\mathrm{hr}$. The average acceleration of the bullet in $\mathrm{m}/{\mathrm{s}}^2$ is

A man of mass $60 \mathrm{kg}$ is standing on a boat of mass $140 \mathrm{kg}$, which is at rest in still water. The man is initially at $20 \mathrm{m}$ from the shore. He starts walking on the boat for $4 \mathrm{s}$ with constant speed $1.5 \mathrm{m}/\mathrm{s}$ towards the shore. The final distance of the man from the shore in meter is

Three stations A, B and C are spaced at equal distance along the track. A train at $160 \mathrm{km} {\mathrm{h}}^{-1}$ passes the station A, driver applies brakes  and reduce its speed uniformly to $40 \mathrm{km} {\mathrm{h}}^{-1}$ at station C. At which part of the track, the train has instantaneous speed of $100 \mathrm{km} {\mathrm{h}}^{-1}$? (Neglect the size of train)

A ball is thrown up, it reaches a maximum height and then comes down. If $t_1$and $t_2$ are the times that the ball takes to be at a particular height, then the time taken by the ball to reach the highest point is

The speed $\left(v\right)$ and time $\left(t\right)$ for an object moving along straight line are related as $t^2+100=2vt$, where $v$ must be