Kinematics equations – quick reckoner of motion equations

Last updated on April 21st, 2023 at 05:02 pm

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, the 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 is the final velocity, a is the acceleration, t is the time taken, and s is the displacement.

Numerical questions – solved

Example (1 )

A dragster starts from rest 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 traveling 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 then 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