Motion in a Straight Line

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 car moves a distance of 200 m. It covers the first half of the distance at speed  $40\frac{km}{hr}$  and the second half of distance at speed v. The average speed is  $48\frac{km}{hr}$ . Find the value of v

A bus travelling the first one third distance at a speed of  $10 \mathrm{km} {\mathrm{h}}^{-1}$, the next one third at  $20 \mathrm{km} {\mathrm{h}}^{-1}$ and the last one – third at  $60 \mathrm{km} {\mathrm{h}}^{-1}$. The average speed of the bus is

A body is moving with velocity  $30\frac{m}{s}$  towards east. After 10 seconds its velocity becomes  $40\frac{m}{s}$  towards north. The average acceleration of the body is

A car covers the first half of the distance between two places at  $40\frac{km}{h}$  and other half at  $60\frac{km}{h}$ . The average speed of the car 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, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

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?