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.