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
(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.
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 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