Video Transcript
How much time is taken for an
object with a speed of 80 meters per second to travel a distance of 300 meters?
So in this question, we’ve been
told that we’ve got an object — let’s say this blob is our object — and it’s moving
at 80 meters per second. So let’s say it’s moving towards
the right at 80 meters per second. We’ve been told that this objective
is moving a distance of 300 meters. So from its start point to its
finish point, the distance the object moves is 300 meters. And we’ve been asked to calculate
the amount of time taken for this subject to travel that distance.
So let’s start by saying that the
distance moved by the object is called 𝑑 and the speed with which the object moves
is called 𝑠. Now that we’ve done this, we can
recall that the speed of an object is defined as the total distance travelled by the
object divided by the time taken for that object to travel that distance. Or in other words, speed is the
rate of change of the distance moved by the object, where rate of change simply
means how much something is changing over a given period of time. In this case, we’re talking about
the rate of change of the distance moved, so how much distance the object is moving
over a given period of time.
Now in this question, we’ve already
been given the speed of the object and the distance moved by the object. However, we’ve been asked to
calculate how long it takes to do that. So what we need to do is to
rearrange this equation here. We need to do this so we can solve
for 𝑡. We can do this by multiplying both
sides of the equation by 𝑡 divided by 𝑠.
This way, on the left-hand side of
the equation, the 𝑠 in the denominator cancels with the 𝑠 up top. And similarly, on the right-hand
side, the 𝑡 in the numerator cancels with the 𝑡 in the denominator. Well that leaves us with 𝑠𝑡 on
the left-hand side and 𝑑 divided by 𝑠 on the right. So when we clean things up a bit,
we can see this a bit more clearly: the amount of time taken for an object to move a
certain distance is equal to that distance moved divided by the speed of the
object.
Now at this point, we can
substitute in the values. So we can say that the time taken
for the object to move the distance is the distance 300 meters divided by the speed
of the object 80 meters per second. Looking very quickly at the units,
we can see that we’ve got meters in the numerator and a meters in the
denominator. So these will cancel. And what we’re left with is one
divided by seconds in the denominator which is equivalent to having seconds in the
numerator.
And hence, our final answer is
going to have the unit of seconds, which is exactly what we want because we’re
trying to find the value of time. And the unit of time is
seconds. So when we do evaluate the fraction
on the right-hand side, we get an answer of 3.75 seconds. That’s the amount of time taken for
the object to move a distance of 300 meters at a speed of 80 meters per second.
