Directions: Answer ALL parts. Show all work and please write neatly.

A crane and box are both initially at rest. At time t=0 s, the crane begins to drive forward at a constant speed of 0.5 m/s, while also lifting the box with an upward acceleration of 1 m/s2. The box does not swing while being lifted by the crane.

part c) Assume that, at t=0s, the horizontal position of the box is x=0 and it has a vertical position of y=0. Derive an equation that describes the vertical position y of the box as a function of the horizontal position, x, of the box.

part d) Does your equation from part c agree with your sketch in part b? Justify your response.

At time t=t1, the crane begins to accelerate forward, reaching a new constant velocity at time t=t2. The box accelerates upwards during the entire time interval t1

part e) The dot below represents the box during the time interval t1

T T T T + - + - - - + + + + + + + + L