Question Video: Finding the Momentum of a Body Moving with Uniform Acceleration at a Given Time Mathematics

A body of mass 12 g accelerated from rest at 19 cm/s². Given that its motion was in a straight line, find its momentum 0.1 minutes after it started moving.

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Video Transcript

A body of mass 12 grams accelerated from rest at 19 centimeters per second squared. Given that its motion was in a straight line, find its momentum 0.1 minutes after it started moving.

The momentum of any body can be calculated by multiplying the mass by velocity. If our mass is in kilograms, we need our velocity to be in meters per second. However, in this case, the mass is in grams. Therefore, we need the velocity in centimeters per second. We know that the mass is 12 grams, and we will need to calculate the velocity. We will do this using our equations of motion or SUVAT equations.

In this question, we don’t know the displacement. We know that the body started from rest. Therefore, the initial velocity is zero centimeters per second. We need to calculate the final velocity which will we call 𝑣. The acceleration is 19 centimeters per second squared. We also know that the time is 0.1 minutes. We can convert this to seconds by multiplying 0.1 by 60. This is equal to six seconds. The equation that doesn’t involve 𝑠 is 𝑣 is equal to 𝑢 plus 𝑎𝑡. Substituting in our values gives us zero plus 19 multiplied by six. The velocity after six seconds is therefore equal to 114 centimeters per second.

To calculate the momentum, we need to multiply 12 by 114. This is equal to 1368. As we’re multiplying the two units, our units for momentum will be gram centimeters per second.

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