Video Transcript
An object moves north at 12 meters
per second for 10 seconds and then stops and stays motionless for 10 seconds before
moving north at 12 meters per seconds for another 10 seconds. What is the object’s average
northward velocity?
Let’s consider the three different
stages of this object’s movement. In the first stage, the object
moves north at 12 meters per second for 10 seconds. We’re then told that the object
stops and stays motionless for 10 seconds. And then, finally, it moves north
at 12 meters per second for another 10 seconds. We’re then asked to calculate the
average northward velocity. So we can recall that average
velocity is equal to the net displacement divided by the total time.
Because we have no change in the
direction, then the magnitude of this net displacement will be the same as the total
distance traveled. We can then work out the distance
in each stage. We can remember that distance is
calculated by speed times time. So in the first stage, we have a
speed of 12 and a time of 10 seconds. Multiplying those together would
give us a distance of 120 meters. In the second stage, when the
object is at rest, the speed is zero and the time is 10 seconds. So the distance traveled will be
zero meters. Finally, we have that distance in
the third stage is the same as the first stage. It’s 12 times 10, which is 120
meters.
When we add these three values
together then, we get that the total distance is 240 meters. In order to apply the formula for
average velocity, we’ll need to calculate the total time. So we have 10 seconds, 10 seconds,
and 10 seconds, which gives us a total time of 30 seconds. We can then fill these values in to
the formula, remembering that we can use the distance in this case because there’s
no change in direction here. So the magnitude of this
displacement is the same as the distance traveled. So 240 over 30 is equal to
eight. And the units here will be meters
per second. And so we can give the answer for
the average northward velocity as eight meters per second.
One other way we could’ve
approached this problem is by using a displacement–time graph. In the first stage, when the object
moved for 10 seconds, remember that we calculated that displacement as 120
meters. It then stayed still for 10
seconds. And finally, it moved another 12
meters per second for 10 seconds. In the first and third sections, we
have a positive motion. And so the graph has a positive
slope. In the middle section, this was a
rest. And so there’s zero slope. If we want to calculate the
velocity at any stage, we can find the slope or gradient of that section. If we want to find the average
velocity, then we can create a line segment between the starting coordinate and the
end coordinate.
We can remember that if we’ve got
two coordinates 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two, we can calculate the slope as 𝑦
two minus 𝑦 one over 𝑥 two minus 𝑥 one. So for the two coordinates then 30,
240 and zero, zero, the slope would be calculated as 240 minus zero over 30 minus
zero. And this simplifies to 240 over 30,
which is eight meters per second. And so we have confirmed the
original answer using a displacement–time graph.
