Video Transcript
If an object moves in a straight
line at a uniform speed, which of the following is correct? (A) The speed becomes a vector
quantity. (B) The speed is the magnitude of
the velocity of the object.
Let’s say that here is our object
and that this is its path of motion. Traveling at a uniform or constant
speed, the object ends up here. So this is the distance the object
travels, while this arrow shows the object’s displacement. Because our object has moved in a
straight line, the distance and the magnitude of the displacement, the length of
this arrow, are the same. Mathematically, we can write that
this way. Distance equals the magnitude of
displacement.
Now, our second answer option,
option (B), talks about the speed of the object as well as its velocity. We can recall general equations for
speed and for velocity. The speed of an object equals the
distance it travels divided by the time taken to cover that distance, while
velocity, a vector quantity, equals displacement divided by time. In this equation for velocity, if
we took the magnitude of displacement, then on the left-hand side we would have the
magnitude of velocity. And now let’s recall that in our
particular scenario, with our object moving in a straight line at a constant speed,
the distance the object travels is indeed equal to the magnitude of its
displacement.
Looking at our equations, that
means we can say the magnitude of displacement here equals this distance here. Going further, for our object
moving in a straight line, the time used to calculate speed is equal to the time
used to calculate the magnitude of velocity. We can therefore write that our
object’s speed is equal to the magnitude of its velocity. This corresponds to answer option
(B). Note that option (A) can’t be
correct because speed is always a scalar, not a vector, quantity. For an object moving in a straight
line at a uniform speed, the speed of the object equals the magnitude of the
object’s velocity.
