How many seconds will it take jeremy to reach the top of

Question

Lab: Displacement, Velocity and Acceleration

INSTRUCTIONS: You may use the back of this paper as your answer sheet if the space provided is insufficient. ALL FINAL ANSWERS MUST BE IN SI UNITS (if computations are required). Use black/blue pens or pencils or pencils only.

1. A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation ??(??) = 1.50 ????²/??²- 0.0500 ????³/??³.

a. What are ??_??(??) and ??_??(??)?

b. What are the magnitudes of velocity and acceleration at t = 8.00s?

2. Jeremy (our cricket) is on a cart that is placed at the bottom of a ramp that is inclined at ?? = 10^?? . Chirpy is at the bottom of the ramp watching Jeremy ride the cart. A kid then pushes the cart up the ramp, giving the cart an initial speed of ??₀ = 4 ??/??.

a. How many seconds will it take Jeremy to reach the top of his motion?

b. How far up the ramp will Jeremy be able to travel?

c. If, after 1 second, Jeremy falls of the cart and breaks his leg and cannot move, what is the distance Chirpy has to travel to save Jeremy from the cart crushing him as the cart rolls down the slope?