Hello, meg24209!

You're expected to know that the velocity is the first derivaitve.A particle moves along the x axis so that at time its position

is given by: .

a) What is velocity of particle at ?

At

When is negative?b) During what time intervals is particle moving to the left?

We have: .

And we find that the velocity is negative for: .

This could be considered a trick question . . .c) What is the total distance traveled by particle from to ?

At

At . . . The particle has moved 4 units to the right.

At . . . The particle has moved 12 units to the left.

Therefore, the particle travelled units.