# Kinematics/Sample Problems

## [edit]

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

a) Find the velocity and acceleration at .

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

Ans) The given curve is displacement versus time curve.

- So, the velocity is given by
- And so, acceleration is
- 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[edit]

**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 with the horizontal, and its muzzle velocity is **600m/sec**, when should the antiaircraft gun fire a shell so as to hit the target??