### Video Transcript

A particle is moving in a straight
line such that its displacement 𝑠 after 𝑡 seconds is given by 𝑠 is equal to two
𝑡 squared minus three 𝑡 plus three meters, where 𝑡 is greater than zero. Determine the velocity 𝑣 as a
function of time.

We are told in the question that
the displacement of a particle 𝑠 is equal to two 𝑡 squared minus three 𝑡 plus
three meters. And we need to find an expression
for the velocity 𝑣. In order to do this, we will need
to differentiate our function, as 𝑣 of 𝑡 is equal to d by d𝑡 of 𝑠 of 𝑡. If the displacement of a body is
given as a function in terms of time, we can differentiate to find an expression for
the velocity. Differentiating two 𝑡 squared
gives us 4𝑡. Differentiating negative three 𝑡
gives us negative three. And differentiating a constant, in
this case three, gives us zero. The velocity is therefore equal to
4𝑡 minus three. As we are differentiating with
respect to 𝑡, 𝑣 is equal to 4𝑡 minus three meters per second. This is an expression for the
velocity as a function of time.