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****–**

*or*

**u)/t**

**v****=**

**u****+**

**at**

**s****=**

**ut****+(1/2)**

**at**^{2}

**v**^{2}

**= u**^{2 }

**+****2**

**as**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/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 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/s

^{2}

(b)

**v**^{2}

**= u**^{2 }

**+****2**

**as**s = (

**v**^{2}

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