Video Transcript
A body of mass 17 kilograms moves
in a straight line with constant acceleration of 1.8 meters per second squared. Its initial velocity is 22.3 meters
per second. Find the increase in its momentum
in the first five seconds.
This question asks us to find the
increase in momentum or change in momentum over a given time period. In order to do this, we need to
work out the difference between its final momentum and its initial momentum. We can express this mathematically
as Δ𝐻 is equal to 𝐻 sub two minus 𝐻 sub one, where Δ𝐻 is the change in momentum,
𝐻 two is the final momentum, and 𝐻 one is the initial momentum. As momentum is equal to mass
multiplied by speed, this can be rewritten as Δ𝐻 is equal to 𝑚𝑣 sub two minus
𝑚𝑣 sub one, where 𝑣 sub two is the final speed, 𝑣 sub one is the initial speed,
and 𝑚 is the mass of the body.
We are told in the question the
initial speed of the body is 22.3 meters per second. We also know that the mass is 17
kilograms. This means we need to begin by
calculating the final speed. We can do this using our equations
of motion, sometimes known as the SUVAT equations.
We know that the initial velocity
is 22.3 meters per second. The acceleration 𝑎 is 1.8 meters
per second squared. And the time period we are
interested in is five seconds. We can therefore calculate the
final velocity 𝑣 using the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡. Substituting in the values of 𝑢,
𝑎, and 𝑡, we have 𝑣 is equal to 22.3 plus 1.8 multiplied by five. 1.8 multiplied by five is equal to
nine. Therefore, 𝑣 is equal to 31.3. The velocity of the body after five
seconds is 31.3 meters per second.
We now have values of 𝑚, 𝑣 sub
one, and 𝑣 sub two. We know the initial speed, final
speed, and the mass of the object. The change in momentum is therefore
equal to 17 multiplied by 31.3 minus 17 multiplied by 22.3. Whilst we could type this straight
into our calculator, we notice that the mass 𝑚 is common to both terms on the
right-hand side. We can therefore rewrite the change
in momentum as 𝑚 multiplied by 𝑣 sub two minus 𝑣 sub one.
In this question, the change in
momentum is equal to 17 multiplied by 31.3 minus 22.3. This simplifies to 17 multiplied by
nine, which in turn is equal to 153. As the mass of the body was
measured in kilograms and the speed or velocities were in meters per second, we use
the standard units of momentum of kilogram meters per second. In the first five seconds of
motion, the momentum of the object increases by 153 kilogram meters per second.
