Question 1: Tx = 34 + 10t - 2t3, where t is in seconds and x in meters.
(a) Plot x as a function of t from t = 0 to t = 3.0 s.
(b) Find the average velocity of the object between 0 and 3.0 s.
(c) At what time between 0 and 3.0 s is the instantaneous velocity zero?
Question 2: An automobile traveling 95 km/ h overtakes a 1.10-km-long train traveling in the same direction on a track parallel to the road. If the train's speed is 75 km/h, how long does it take the car to pass it, and how far will the car have traveled in this time? What are the results if the car and train are traveling in opposite directions?
Question 3: The position of an object is given by x = At + Bt2, where x is in meters and t is in seconds.
(a) What are the units of A and B?
(b) What is the acceleration as a function of time?
(c) What are the velocity and acceleration at t = 5.0 s?
(d) What is the velocity as a function of time if x = At + Bt-3?
Question 4: A toy rocket moving vertically upward passes by a 2.0-m-high window whose sill is 8.0 m above the ground, the rocket takes 0.15 s to travel the 2.0 m height of the window. What was the launch speed of the rocket, and how high will it go? Assume the propellant is burned very quickly at blastoff.
Question 5: Given v(t) = 25 + 18t, where v is in m/s and t is in s, use calculus to determine the total displacement from t1 = 1.5 s to t2 = 3.1 s.