# 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+andu)/2s=[(u+v)/2]tacceleration,a=(v–oru)/tv=u+ats=ut+(1/2)at^{2}v^{2}= u^{2 }+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/s

^{2}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)at**

^{2}= 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/s

^{2}

(b)

**v**^{2}

**= u**^{2 }

**+****2**

**as**s = (

**v**^{2}

**– u**^{2}) / (2a) = (35×35 – 20×20) / (2×2750) = 0.15 m