1. Cars A and B are moving in opposite directions along a straight road. They pass each other at time t = 0. Their velocities v are given as a function of time t in the graph above. The distance between the cars at t = 8 s is
(B) 24 m
(C) 48 m
(D) 96 m
(E) 192 m
2. A particle is moving along the y-axis. The particle's position as a function of time is given by y = at3 - βt +Φ，where a= l m/s3， β = 4 m/s, and ¢= 3 m. What is the particle's acceleration at time t = 3.0 s?
(A) 6.0 m/s2
(B) 9.0 m/s2
(C) 18 m/s2
(D) 23 m/s2
(E) 27 m/s2
3. Two stones, represented in the figure above, are thrown from the same height with the same initial speed. Stone A is thrown vertically downward and stone Bis thrown horizontally. If the stones are thrown at the same time and air resistance is negligible, which of the following is true?
(A) The two stones will reach the ground at the same time with the same speed.
(B) The two stones will reach the ground at the same time but with different speeds.
(C) Stone A will reach the ground first, but stone B will have the greater speed just before hitting the ground.
(D) Stone A will reach the ground first, but the two stones will have the same speed just before they hit the ground.
(E) Stone A will reach the ground first, and will have the greater speed just before hitting the ground.
1. A projectile is launched from the back of a cart of mass m that is held at rest, as shown above. At time t = 0, the projectile leaves the cart with speed v0 at an angle θ above the horizontal. The projectile lands at point P. Assume that the starting height of the projectile above the ground is negligible compared to the maximum height reached by the projectile and the horizontal distance traveled.
(a) Derive an expression for the time tp at which the projectile reaches point P. Express your answer in terms of v0 , θ, and physical constants, as appropriate.
(b) On the axes below, sketch the horizontal component vx and the vertical component vy of the velocity of the projectile as a function of time t from t = 0 until t = tp. Explicitly label the vertical intercepts with algebraic expressions.