The position vector of a particle changes with time according to the relation $\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j$. What is the magnitude of the acceleration at $t = 1$ ?
$40$
$100$
$25$
$50$
The figure shows the velocity $(v)$ of a particle plotted against time $(t)$
A particle starts from origin at $t=0$ with a velocity $5.0 \hat{ i }\; m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3.0 \hat{ i }+2.0 \hat{ j })\; m / s ^{2} .$
$(a)$ What is the $y$ -coordinate of the particle at the instant its $x$ -coordinate is $84 \;m$ ?
$(b)$ What is the speed of the particle at this time?
A projectile is projected with speed $u$ at an angle $\theta$ with the horizontal. The average velocity of the projectile between the instants it crosses the same level is ............