At time $t =0$ a particle starts travelling from a height $7\,\hat{z} cm$ in a plane keeping $z$ coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3\,t$ and $5\,t^{3}$ respectively. At $t =1\,s$ acceleration of the particle will be.

A particle moves along a straight line in such a way that it’s acceleration is increasing at the rate of $2 m/s^3$. It’s initial acceleration and velocity were $0,$ the distance covered by it in $t = 3$ second is  ........ $m$

$A$ body $A$ is thrown vertically upwards with such a velocity that it reaches a maximum height of $h$. Simultaneously another body $B$ is dropped from height $h$. It strikes the ground and does not rebound. The velocity of $A$ relative to $B v/s$ time graph is best represented by : (upward direction is positive)

A particle starts from the origin at $\mathrm{t}=0$ with an initial velocity of $3.0 \hat{\mathrm{i}} \;\mathrm{m} / \mathrm{s}$ and moves in the $x-y$ plane with a constant acceleration $(6.0 \hat{\mathrm{i}}+4.0 \hat{\mathrm{j}}) \;\mathrm{m} / \mathrm{s}^{2} .$ The $\mathrm{x}$ -coordinate of the particle at the instant when its $y-$coordinate is $32\;\mathrm{m}$ is $D$ meters. The value of $D$ is

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects

The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be