# Kinematics & Projectile Motion

The average speed vav and average velocity of a body during a time interval is defined as,

Vavg= Total Distance / Total Time

Instantaneous speed and velocity are defined at a particular instant and are given by

**Note:**

(a) A change in either speed or direction of motion results in a change in velocity

(b) A particle which completes one revolution, along a circular path, with uniform speed is said to possess zero velocity and non-zero speed.

(c) It is not possible for a particle to possess zero speed with a non-zero velocity.

Average acceleration is defined as the change in velocity over a time interval t.

The instantaneous acceleration of a particle is the rate at which its velocity is changing at that instant.

**Kinematical Equations:**

The three equations of motion for an object with constant acceleration are given below.

Here 𝑢 is the initial velocity, v is the final velocity, a is the acceleration, s is the displacement travelled by the body and t is the time.

Note: Take ‘+ve’ sign fora when the body accelerates and takes ‘–ve’ sign when the body decelerates.

The displacement by the body in nth second is given by,

**All Graphs from Kinematics**

**Relative Velocity**

Relative Velocity is the velocity of a moving body with respect to another moving body

1) Bodies moving in the same direction; a –b

2) Bodies moving in opposite directions; a + b

3) Bodies moving and inclined at an angle θ to each other, then:

Motion in a Straight Line: Moves along one co-ordinate axis

Motion in a Plane: Moves in a plane with 2d co-ordinate axis.

Motion in Space: Moves in Space with 3d co-ordinate axis.

Projectile Motion, Motion in 2 Dimensions / Motion in a Plane

**Projectile motion in a plane:**

If a particle having initial speed u is projected at an angle θ (angle of projection) with x-axis, then,

**Motion on an inclined plane:**

1) Perpendicular vector: At the top of the inclined plane (t = 0, u = 0 and a = g sinθ), the equation of motion will be,

2) If time taken by the body to reach the bottom is t,

3) The velocity of the body at the bottom