Kinematic Equations for Uniformly Accelerated Motion

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 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, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

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?

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

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?

The water drops fall at regular intervals from a tap $5\hspace{0.17em}\mathrm{m}$ above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. How far above the ground is the second drop at that instant?  (Take $g=10\hspace{0.17em}\mathrm{m} {\mathrm{s}}^{-\mathrm{2}}$)