A 100 kg box as showsn above is being pulled along the x axis by a student. the box slides across a rough surface, and its position x varies with time t according to the equation x=.5t^3 +2t where x is in meters and t is in seconds.

(a) Determine the speed of the box at time t=0
(b) determine the following as functions of time t.

a) 2 m/s

b) i)

ii)

Explanation:

The function for distance is

We know that:

Velocity =

Acceleration =

To find speed at time t = 0, we derivate the distance function:

Substitute t = 0 in velocity function:

Velocity at t = 0 will be 2 m/s.

To find the function for Kinetic Energy of the box at any time, t.

We know that

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up