Instantaneous Velocity and Speed

The coordinates of a moving particles at any time $t$ are given by  $x=\alpha t^3$ and $y=\beta t^3$ . The speed of the particle at time $t$ is given by –

The coordinates of a moving particles at any time $t$ are given by  $x=\alpha t^3$ and $y=\beta t^3$ . The speed of the particle at time $t$ is given by –

A particle is moving with a constant speed in a circle. What is the magnitude of average velocity after one fourth rotation?

The speed of a jeep is $125 \mathrm{km}/\mathrm{h}$. It takes $120 \mathrm{minutes}$ to cover a certain distance. Find the distance in metres.

If the position of a particle is $x= \left(6t^2-t^3\right) \mathrm{m}$, then find the position of the particle when velocity is maxima.

The figure shows the distance-time graph for the motion of two vehicles A and B. Which one of them is moving faster?

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Consider the motion of an athlete running along a circular track. The radius $\left(r\right)$ of the circular track. Assume that the athlete starts at A. If the athlete runs the first quarter AB  in $11 \mathrm{s}$, BC in $22 \mathrm{s}$, CD in $33 \mathrm{s}$, and DA in $44\mathrm{s}$, find the speed and velocity in each of the following cases.

An ant runs from an ant-hill in a straight line so that its velocity is inversely proportional to the distance from the centre of the ant-hill. When the ant is at a point  A at a distance $1\mathrm{m}$ from the centre of the hill, its velocity is $2\mathrm{cm}/\mathrm{s}$. Point B is at a distance of $2\mathrm{m}$ from the centre of the ant-hill. The time taken by the ant to run from A to B is

A point moves with uniform acceleration and its initial speed and final speed are $1 {\mathrm{ms}}^{-1}$ and $2 {\mathrm{ms}}^{-1}$ respectively then, the space average velocity over the distance moved is(in ${\mathrm{ms}}^{-1}$):-

The distance travelled by a body moving along a straight line at time $t$ is given by $S=3-4t+5t^2$. The initial velocity of the body is

A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then, the magnitude of the average velocity for its motion from $A$ to,

A car moving on a straight line covers a distance at speed $\mathrm{v}$ and the return journey with a speed of $2\mathrm{v}$ Find (i) average speed and (ii) mean speed.

The ratio of the numerical values of the average velocity and average speed of a body is always unity or more.

Given $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+\hat{j}$. The magnitude of component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ is

From a building two balls A and B are thrown such that A is thrown upwards and B downwards with the same speed (both vertically). If $v_A \mathrm{and}\mathrm{ }{v}_B$ are their respective velocities on reaching the ground then: $v_A=v_B$.

Which year did the First Fleet arrive in Australia, marking the beginning of European settlement?

During which stage of human development does the most rapid physical growth occur?

Which of the following variables is NOT continuous?

What is the interval between two high tides?