### Video Transcript

The position of an object changes
as a function of time according to 𝑥 of 𝑡 equals negative three 𝑡 squared
meters. What is the object’s velocity when
𝑡 equals one second? What is the object’s speed when 𝑡
equals one second?

Given a function describing an
object’s position as a function of time, we want to know its velocity when 𝑡 is
equal to one second and its speed at that same time. In other words, we want to solve
for its instantaneous velocity and instantaneous speed. We can recall that an object’s
instantaneous velocity is equal to the derivative of its position with respect to
time. In our case, we’re given 𝑥 or
position as a function of time and can plug in for that expression. When we take its derivative with
respect to time, we find a result of negative six times 𝑡, now with units of meters
per second. This is the instantaneous velocity
of our object at a general time 𝑡. But we want to solve for that
velocity when time is equal to one second. When 𝑡 is equal to one second, our
instantaneous velocity is negative six times one meters per second, or negative six
meters per second. That’s our instantaneous velocity
when 𝑡 equals one second. Now what about its speed at that
time?

We can recall that instantaneous
speed is a scalar quantity. And it’s equal to the magnitude of
instantaneous velocity. This means that the instantaneous
speed of our object, when 𝑡 is equal to one second, is equal to the absolute value
of negative six meters per second. This simplifies to six meters per
second. That’s the object’s instantaneous
speed when time equals one second.