Enter the masses and velocities of two colliding objects into the calculator to determine the collision speed. The calculator assumes a perfectly inelastic collision where the two objects move together after the collision.

Collision Speed Formula

The following formula is used to calculate the collision speed of two objects in a perfectly inelastic collision.

CS = |(m1 * v1 + m2 * v2) / (m1 + m2)|

Variables:

  • CS is the collision speed (meters per second, m/s)
  • m1 is the mass of object 1 (kilograms, kg)
  • v1 is the velocity of object 1 (meters per second, m/s)
  • m2 is the mass of object 2 (kilograms, kg)
  • v2 is the velocity of object 2 (meters per second, m/s)

To calculate the collision speed, add the product of the mass and velocity of the first object to the product of the mass and velocity of the second object. Then, divide the result by the sum of the masses of both objects. The absolute value is taken to ensure the speed is non-negative.

What is Collision Speed?

Collision speed is the speed at which two objects move together after a perfectly inelastic collision, where they stick together and move as a single object. This speed is a result of the conservation of momentum, assuming no external forces act on the system of the two objects. It is an important concept in physics, particularly in the study of momentum and collisions.

How to Calculate Collision Speed?

The following steps outline how to calculate the Collision Speed.

  1. First, determine the mass of object 1 (m1) in kilograms.
  2. Next, determine the velocity of object 1 (v1) in meters per second.
  3. Then, determine the mass of object 2 (m2) in kilograms.
  4. After that, determine the velocity of object 2 (v2) in meters per second.
  5. Use the formula from above to calculate the Collision Speed (CS).
  6. Finally, calculate the Collision Speed (CS) in meters per second.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Mass of object 1 (m1) = 1500 kg

Velocity of object 1 (v1) = 20 m/s

Mass of object 2 (m2) = 1000 kg

Velocity of object 2 (v2) = -15 m/s (opposite direction)