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 ?
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 . . . The particle has moved 4 units to the right.
At . . . The particle has moved 12 units to the left.
Therefore, the particle travelled units.