Motion With Constant Acceleration

An object moving with uniform acceleration has a velocity of $12.0 \mathrm{cm} {\mathrm{s}}^{-1}$ in the positive $x$ direction when its $x$ coordinate is $3.00 \mathrm{cm}$. If its $x$ coordinates $2.00 \mathrm{s}$ later is $-5 \mathrm{cm}$, what is its acceleration?

At a distance $L=400 \mathrm{m}$ from the traffic light brakes are applied to a locomotive moving at a velocity $v=54 \mathrm{km} {\mathrm{hr}}^{-1}$. Determine the position of the locomotive relative to the traffic light $1$ minute after the application of the brakes if its acceleration is $- 0.3 \mathrm{m} {\mathrm{s}}^{-2}$.

A body starts from rest, what is the ratio of the distances traveled by the body during the 4^th and 3^rd seconds?

A boy standing at the top of a tower of 20 m height drops a stone. Assuming  $g=10\mathrm{\hspace{0.17em}}\mathrm{m} {\mathrm{s}}^{-2}\hspace{0.17em},\hspace{0.17em}$ the velocity with which it hits the ground is

A particle has initial velocity $(3\widehat{i}+4\widehat{j})$ and has acceleration $(0.4\widehat{i}+0.3\widehat{j}).$ Its speed after 10 s is:

A particle starts its motion from rest under the action of a constant force. If the distance covered in the first $10$ seconds is $S_1$ and that covered in the first $20$ seconds is  $S_2$, then:

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10\mathrm{m} {\mathrm{s}}^{-1}$  to  $20\mathrm{m} {\mathrm{s}}^{-1}$ while passing through a distance $135 \mathrm{m}$ in $t$ seconds. The value of $t$ is:

The position $x$ of a particle with respect to time $t$ along $x$-axis is given by, $x=9t^2-t^3$ where, $x$ is in meters and $t$ is in seconds. What will be the position of this particle when it achieves maximum speed along the $+ve x$ direction?

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

A car moving with a speed of $40 \mathrm{km} {\mathrm{h}}^{-1}$ can be stopped by applying brakes at least after $2 \mathrm{m}$. If the same car is moving with a speed of $80 \mathrm{km} {\mathrm{h}}^{-1}$, what is the minimum stopping distance?

A car is moving along a straight road with a uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance with velocity $30{\text{\hspace{0.17em}km hr}}^{-1}$ and $40{\text{\hspace{0.17em}km hr}}^{-1}$ respectively. The velocity of the car midway between $P$ and $Q$ is

A ship of mass  $3\times {10}^7 \mathrm{kg}$  initially at rest, is pulled by a force of $5\times {10}^4 \mathrm{N}$  through a distance of $3 \mathrm{m}$. Assuming that the resistance due to water is negligible, the speed of the ship is

A body falling freely from a given height $H$ hits an inclined plane in its path at a height $h$. As a result of this impact, the direction of the velocity of the body becomes horizontal. For what value of $\left(\frac{h}{H}\right)$ the body will take maximum time to reach the ground?

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{d}{2}$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as

A body starts from $20 \mathrm{m}/\mathrm{s}$. If its acceleration is $2 \mathrm{m}/{\mathrm{s}}^2$, then velocity of the body after $10 \mathrm{seconds}$ is

The velocity of train decreases uniformly from $50 \mathrm{km} {\mathrm{h}}^{-1}$ to $10 \mathrm{km} {\mathrm{h}}^{-1}$ in $2$ hours. The distance travelled by the train during this process is

Two cars, one travelling at$54 \mathrm{km} {\mathrm{h}}^{-1}$  and the other at $90 \mathrm{km} {\mathrm{h}}^{-1}$move towards each other along a narrow road. When they are $150 \mathrm{m}$ apart, both the drivers apply the brakes simultaneously. The motion of each car is retarded at $3 \mathrm{m} {\mathrm{s}}^{-2}$ and the collision is avoided. Find the distance between the cars when they come to rest.