# Kinematics/Sample Problems

## Sample problem related to curvilinear motion

Q.1) The motion of a body varies with the following equation:

$S=t^{3}-3t^{2}+6t+1\,\!$

a) Find the velocity and acceleration at $t=4secs\,\!$ .

b) Find the maximum or minimum velocity experienced during its motion.

Ans) The given curve is displacement versus time curve.

$S=t^{3}-3t^{2}+6t+1\,\!$
So, the velocity is given by
$V={\frac {ds}{dt}}=3t^{2}-6t+6\,\!$
And so, acceleration is
$a={\frac {d^{2}s}{dt^{2}}}=6t-6\,\!$
Proceed for the problem by substituting the instant at which you need the variables..
For maximum or minimum velocity, use the concepts of MAXIMA AND MINIMA from mathematics, which makes use of derivatives.

## Projectile motion

Q.2) An F-22 bomber is under a training session in the deserts of Iran. It is moving horizontally parallel to the ground at a speed of 1000kmph and at an altitude of 2400 meters. to bomb an target which is an mimic of an antiaircraft gun.

a)At what point from the antiaircraft gun should the bomber release the bomb so as to hit the target?

b)Now, if this becomes a real warfare scenario, and the anti aircraft gun's gears are blocked so that it is fixed at an angle of ${60}^{o}\,\!$  with the horizontal, and its muzzle velocity is 600m/sec, when should the antiaircraft gun fire a shell so as to hit the target??