# Question Video: Calculating the Momentum of a Particle Given its Mass and Velocity Mathematics

Find the momentum of a body with a mass of 33 kg moving with a velocity of 18 km/h. Give your answer in gram-centimeters per second.

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### Video Transcript

Find the momentum of a body with a mass of 33 kilograms moving with a velocity of 18 kilometers per hour. Give your answer in gram centimeters per second.

We begin by recalling that the momentum of a body can be calculated by multiplying its mass 𝑚 by its velocity 𝑣. In this question, we’re asked to give our answer in gram centimeters per second. This means that we need to know the mass of the body in grams and its velocity in centimeters per second. We are given the mass in kilograms, and we know that there are 1,000 grams in one kilogram. Multiplying 33 by 1,000, we see that the mass of the body is 33,000 grams.

We are given the velocity in kilometers per hour. There are 100,000 centimeters in one kilometer and 3,600 seconds in one hour. In order to convert 18 kilometers per hour into centimeters per second, we need to multiply 18 by 100,000 over 3,600. This is equal to 500 centimeters per second. We can then calculate the momentum by multiplying 33,000 by 500. This is equal to 16,500,000.

The momentum of a body of mass 33 kilograms moving with a velocity of 18 kilometers per hour is 16,500,000 gram centimeters per seconds.