A new motion detector is used to graph the position of a sports car. If the themotion detector is not callibrated properly, it might give unrealistic graph data. The position of the car is described by the function S= 2t^3-21t^2 + 60t, tE [0,6], where s is measured in meters and t in seconds. it is known the largest acceleration is 12 m/s ^2.

Can some one double check this ? and help me

a) WHat is its initial velocity? ---60

b)When is the car at rest? t=0

c)When is the car moving in the forward direction? *******Can someone explain to me how to get this?

d)draw a diagram ----

e)Find the total distance traveled by the car in the first 6 seconds----36

f)Find the max acceleration of the car? a = 12t-42 a=30