1) The velocity of an object is given by v(t) = 9t2 - 4t + 6. At t = 1 s the position of the object is at 10 m. Calculate the acceleration equation and position equation for the object.
2) Derive the equation, v2 = v02 + 2aΔx, by combining the other two main motion equations given in class.
3) Mitch is riding a stolen recumbent bicycle at a constant velocity of 40 m/s. At some point in time, he applies the brakes which make the recumbent slow to a stop over a period of 5.0 s.
(a) What is the acceleration of the bicycle?
(b) How far does the bicycle travel before coming to a stop?
4) A Cessna Jet (call number 90-RC) has a lift-off velocity of 120 km/hr. The runway that 90-RC takes off from is 240 m long.
(a) What is the minimum acceleration that the jet has to have in order to take off before it reaches the end of the runway?
(b) How long does it take for 90-RC to take off?
5) A train is traveling at 100 m/s. The engineer applies the brakes because he sees a recumbent bicycle on the tracks ahead. The brakes cause an acceleration of -2.2 m/s2. The engineer applies the brakes when the train is 960 m from the bicycle. How long does it take the train to reach the bicycle?
6) An object has a position equation of
x(t) = -2/3t3- 4t2 +6t + 4 .
(a) At what times does the object have a velocity of zero?
(b) What is the location of the object when its acceleration is zero?'
7) While chasing Mitch for destroying his bicycle. Skid does the following in his Pinto:
1. He starts from rest and accelerates at 0.6 m/s2 for 15 s.
2. Travels at a constant velocity for 2 minutes.
3. Slows to a stop with an acceleration of -0.75 m/s2.
What is the total distance that Skid travels?
8) A juggling bag is thrown straight up into the air and is caught 2 s later.
(a) What is the initial velocity of the ball?
(b) Calculate the maximum height that it reaches.
9) A coyote with and anvil falls off of a high cliff. Luckily the coyote has a parachute. The chute opens and they both fall at a constant velocity of 10 m/s. When they are 50 m above the ground, the coyote drops the anvil.
(a) How long does it take the anvil to hit the ground?
(b) What is the velocity of the anvil right before it hits the ground?
10) Mitch is skydiving. He Jumps out of a plane and reaches a terminal velocity (constant velocity) of 20 m/s. When he is 1000 m above the ground, Skid, standing directly below Mitch, fires a rocket launcher at Mitch. The rocket has an initial velocity of 125 m/s.
(a) How much time does Mitch have to figure out how to survive this predicament?
(b) Assuming Mitch does not have his wits about him, at what location above the ground will the rocket intersect with him?