Speed, Velocity and Acceleration

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 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

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 –

In $1.0 \mathrm{s}$, a particle goes from point $A$ to point $B$, moving in a semicircle of radius $1.0 \mathrm{m}$ (see figure). The magnitude of the average velocity is

For the given acceleration-time graph, corresponding velocity-time graph will be: (initial velocity$=-6{\mathrm{ms}}^{-1}$)

The relation between position $\left(x\right)$ and time $\left(t\right)$ are given below for a particle moving along a straight line. Which of the following equation represents uniformly accelerated motion? [where $\alpha$ and $\beta$ are positive constants]

The distance $\left(x\right)$ travelled by a particle in time, $t$, is given by $t=4x^2+5x$. If '$v$' is the velocity, then acceleration will be :

An object is moving with variable speed, then

If a particle is moving along straight line with increasing speed, then

A body is moving with variable acceleration (a) along a straight line. The average acceleration of body in time interval $t_1$ to $t_2$ is

When the velocity of body is variable, then

A particle moves in $xy-$plane from positions $\left(2\mathrm{m}, 4\mathrm{m}\right)$ to $\left(6\mathrm{m}, 8\mathrm{m}\right)$ in $2 \mathrm{s}$. Magnitude and direction of average velocity is

The speed of light is $3.0\times {10}^8 \mathrm{m}{ \mathrm{s}}^{-1}$, then the distance covered by light in $2.00$ nano seconds will be -

A boy starts from a point $A$, travels to a point $B$ at a distance of $3 \mathrm{km}$ from $A$ and returns to $A$. If he takes two hours to do so, his speed is

The velocity time graph of a body is shown in figure.

It implies that at point $B$

The acceleration of a moving body can be found from