Kinematics in One and Two Dimensions

The figure shows the $v-t$ graph of a particle moving in a straight line. Starting from rest, the time after which the particle returns to its starting position is

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The velocity-time graph of the particle moving along a straight line is shown. The rate of acceleration and deceleration is constant and it is equal to $5 \mathrm{m} {\mathrm{s}}^{-2}$. If average velocity during the motion is $20 \mathrm{m} {\mathrm{s}}^{-1}$, then find the value of $t$

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 bus is moving on a straight road towards north with a uniform speed of  $50 \mathrm{km} {\mathrm{h}}^{-1}$  turns through  $90°$ anticlockwise. If the speed remains unchanged after turning , the increase in the velocity of bus in the turning process is:

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