Kinematics equations – quick reckoner of motion equations

Last updated on May 20th, 2021 at 04:34 am

Here we have listed down important equations (or formula sets) related to Kinematics. You will get kinematics equations on position, displacement, total displacement, average velocity, instantaneous velocity, average speed, instantaneous speed, average acceleration, instantaneous acceleration, velocity from acceleration, position from velocity, free-fall equations, etc.

Kinematics equations – cheat sheet

kinematic equations for uniformly accelerated motion (6 equations)

If the acceleration of an object is uniform, the following equations apply to its motion:

average velocity = (v + u)/2 and s =[(u + v)/2]t

acceleration, a =(v – u)/t or v = u + at

s = ut +(1/2)at²

v² = u² + 2as

where u is the initial velocity, v the final velocity, a the acceleration, t the time taken, and s the displacement.

Numerical questions – solved

Example (1 )

A dragster starts from rests and accelerates at 25 m/s² for 4 s.
Calculate:
(a) the final velocity
(b) the distance traveled.

Answer:

(a) v = u + at = 0 + (25×4) = 100 m/s

(b) s = ut +(1/2)at² = 0 + (1/2)x25x4x4 = 200 m

Example (2 )

A ball travelling at 20 m s−1 is hit by a bat and returned along its original path but in the opposite direction at 35 m/s. If the ball was in contact with the bat for 0.02 s calculate:
(a) the acceleration of the ball during the hit
(b) the distance moved by the ball during the hit.

Answer:

(a) a =(v – u)/t = [35 – (-20)]/0.02 = 2750 m/s²

(b) v² = u² + 2as
s = (v² – u² ) / (2a) = (35×35 – 20×20) / (2×2750) = 0.15 m