Q12) A car is traveling with speed v0 when it begins to speed up at a rate of Δv every second. After t1 seconds, the car travels with zero acceleration for t2 seconds. Which of the following is a correct expression for the displacement of the car during this motion? Hint: Δv every second is the definition of acceleration which is acceleration = change in velocity / unit of time (s); thus in this problem, a = Δv

Using the kinematics equation and using only the known variables, all answers in terms on Δv, t1, t2, and v0 only.

a) Derive an equation for displacement x for the 1st part of the motion.
b) Derive an equation for the final velocity of the car after the 1st part of the motion.
c) Derive an equation for the displacement for the 2nd part of the motion
d) Derive an equation for the total displacement of the car.
e) Sketch the position vs time graph of this car. (SKETCH in AP means just the general shape of the graph; don’t need to have the exact number, just the shape of the curve/line)