### Video Transcript

A particle is moving in a straight
line such that its displacement ๐ after ๐ก seconds is given by ๐ is equal to two
๐ก squared minus three ๐ก plus three meters, where ๐ก is greater than zero. Determine the velocity ๐ฃ as a
function of time.

We are told in the question that
the displacement of a particle ๐ is equal to two ๐ก squared minus three ๐ก plus
three meters. And we need to find an expression
for the velocity ๐ฃ. In order to do this, we will need
to differentiate our function, as ๐ฃ of ๐ก is equal to d by d๐ก of ๐ of ๐ก. 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 ๐ก squared
gives us 4๐ก. Differentiating negative three ๐ก
gives us negative three. And differentiating a constant, in
this case three, gives us zero. The velocity is therefore equal to
4๐ก minus three. As we are differentiating with
respect to ๐ก, ๐ฃ is equal to 4๐ก minus three meters per second. This is an expression for the
velocity as a function of time.