How to Calculate Velocity and Acceleration

Kinematics is the study of motion without considering forces. The four SUVAT equations (named for the variables they use) let you solve for any unknown when you know three of the five variables: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).

The Four SUVAT Equations

v = u + at
s = ut + Β½atΒ²
vΒ² = uΒ² + 2as
s = Β½(u + v)t

Defining the Variables

  • s = displacement (m)
  • u = initial velocity (m/s)
  • v = final velocity (m/s)
  • a = acceleration (m/sΒ²)
  • t = time (s)

Step-by-Step Example: Free Fall

A ball is dropped from rest (u = 0) from a 45 m building. How long does it take to hit the ground, and what is the impact velocity? (g = 9.81 m/sΒ²)

Find time: s = ut + Β½atΒ² 45 = 0 + Β½ Γ— 9.81 Γ— tΒ² tΒ² = 45 / 4.905 = 9.17 t = 3.03 seconds

Find impact velocity: v = u + at v = 0 + 9.81 Γ— 3.03 = 29.7 m/s (about 66 mph)

Braking Distance Example

Car at 60 mph (26.8 m/s) brakes with deceleration of βˆ’7.5 m/sΒ²:

vΒ² = uΒ² + 2as β†’ 0 = 26.8Β² + 2(βˆ’7.5)s s = 26.8Β² / (2 Γ— 7.5) = 718.24 / 15 = 47.9 meters (about 157 feet)

Average vs. Instantaneous Velocity

Average velocity = total displacement / total time (covers the whole journey) Instantaneous velocity = velocity at a specific moment (what your speedometer reads)

Use our kinematics calculator to solve for any SUVAT variable.