Derivation of second equation of motion is:

The distance $x$ covered in time $t$ by a body having initial velocity ${ v } _{ 0 }$ and having constant acceleration $a$ is given by $x={ v } _{ 0 }t+1/2a{ t }^{ 2 }$. This result follows from :

A ladder of length 10 m and mass 20 kg (and with uniform mass distribution) leans against a slippery vertical wall. The ladder makes an angle of $30^{\circ}$ with respect to the vertical. Friction between the ladder and the ground prevents it from sliding downwards. What is the magnitude of the force exerted on the ladder by the wall?
$[Take \sqrt { 3 } =1.732;g=10{ m/s }^{ 2 }]$

For a body moving with an initial velocity $u$ and uniform acceleration $a$. Find the displacement of the body in time t.

How is the distance related with time for the motion under uniform acceleration such as the motion of a freely falling body starting from rest?

The correct equation of motion is :

In the equation of motion, $S = ut + 1/2 at^2$, S stands for

Gradient of line of displacement-time graph gives the :

Gradient of line of velocity-time graph gives :

Two trains A and B each of length 400m Are moving on two parallel tracks The same direction (while A is ahead of B) With same speed 72 km / h.The driver of B decides to overtake And accelerate by $1m/{ s }^{ 2 }$. If after 50 seconds B Just brushes past A, Calculate the original distance between A and B

At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the platform with $a =  - 0.5m/{s^2}$ relative to the platform. The platform moves with a constant speed $v =  + 1.0m/s$ relative to the stationary floor. In $4.0$ seconds, how much will the child have been displaced relative to the floor?

An open lift is moving upwards with velocity $10m/s$. It has an upward acceleration of $2m/{s^2}$. A ball is projected upwards with upwards with velocity $20m/s$ relative to the ground. Find the time when the ball again meets the lift.

An elevator car whose floor-to-ceiling distance is equal to 2.7m starts ascending with a constant acceleration $1.2m/{s^2};2.0s$ after the start a bolt begins falling from the ceiling of the car. Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

A boy sitting on the top most berth in the compartment of a train which is just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about 2 m. The apple will fall

The distance covered by a body moving alone-X-axis with initial velocity 'u' and uniform acceleration 'a' is given by $\displaystyle x=ut+\frac{1}{2}at^{2}$. This result is a consequence of

A cart begins from rest at the top of a long incline and rolls with a constant acceleration of $2m/s^{2}$. How far has the cart moved along the incline after rolling for $3$ seconds?

A car was travelling at a speed of 10 m/s. After the brakes were applied, it start to decelerate at a rate of 2 $m/s^2$ and finally came to rest. Find the distance traveled by the car before coming to rest.

The initial velocity of a particle (at $t = 0$) is $u$ and the acceleration by $f$ of particle at time $t$ is given $f=at$. Where $a$ is a constant which of the following relation for velocity $v$ of particle after time $t$ is turn