Video Transcript
A car moves a distance of 2200
meters along a winding road for 50 seconds. Its displacement is 800 meters. How much greater is the speed of
the car than the magnitude of the velocity of the car?
In this question, we are asked to
find how much greater the speed of the car is than the magnitude of the velocity of
the car. In order to answer this question,
we need to work out two things: the speed of the car and the magnitude of its
velocity. Let’s start by defining what both
of these terms mean.
The speed of the car is equal to
the distance traveled divided by the time it takes to travel that distance. On the other hand, the magnitude of
the velocity is equal to the displacement of the car divided by the time taken to
reach this displacement. Both of these equations look very
similar, but it is important to remember that they are not the same. The speed depends on the distance
traveled by the car, whilst the velocity depends on the car’s displacement. Let’s recap the difference between
distance and displacement.
The distance traveled by the car is
equal to the total length of the path that it took. In this case, it’s equal to the
total length of this winding road, which we are told is 2200 meters. The displacement of the car is
simply the shortest straight-line distance between its starting position and its
final position. In this case, the displacement is
800 meters. Remember that although velocity and
displacement are vector quantities, in this question, we’re only concerned with
their magnitudes. We won’t need to consider the
direction of the displacement in order to find the magnitude of the car’s
velocity.
Now, the time taken for the car to
travel a distance of 2200 meters and reach a displacement of 800 meters is equal to
50 seconds. First, let’s find the speed that
the car travels at. The speed of the car is equal to
the distance traveled, 2200 meters, divided by the time it takes, 50 seconds. So, the speed is equal to 44 meters
per second. Now, let’s find the magnitude of
the velocity of the car. The magnitude of the velocity of
the car is equal to the car’s displacement, 800 meters, divided by the time taken to
reach this displacement, 50 seconds. This gives us a value of 16 meters
per second. So, we have found that the car has
a speed of 44 meters per second and a velocity of magnitude 16 meters per
second.
The question is asking us to find
how much greater the speed of the car is than the magnitude of its velocity. We can do this by subtracting the
magnitude of the velocity from the speed. This gives us 44 meters per second
minus 16 meters per second, which is equal to 28 meters per second. This tells us that the speed is 28
meters per second greater than the magnitude of the velocity.
