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?

A particle goes from $A$ to $B$ with a speed of $40 \mathrm{km} {\mathrm{h}}^{-1}$ and $B$ to $C$ with a speed of $60 \mathrm{km} {\mathrm{h}}^{-1}$. If $AB=6\hspace{0.17em}BC$, the average speed in $\mathrm{km} {\mathrm{h}}^{-1}$ between $A$ and $C$ is

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

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?