ap mechanics 2020_在线真题试卷与模拟练习_ap mechanics 2020

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（含图）

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

A particle is moving along the y-axis. The particle's position as a function of time is given by $$y = \alpha t^3 - \beta t + \phi$$, where $$\alpha = 1\ \text{m/s}^3$$, $$\beta = 4\ \text{m/s}$$, and $$\phi = 3\ \text{m}$$. What is the particle's acceleration at time $$t = 3.0\ \text{s}$$?

（含图）

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 B is thrown horizontally. If the stones are thrown at the same time and air resistance is negligible, which of the following is true?

Questions 4-6

（含图）

A car is traveling clockwise around a circular racetrack of radius 1440 m. When the car is at the northernmost point on the circle, as shown above, it has a speed of 36.0 m/s and is slowing down at a rate of 1.20 m/s² .

The direction of the acceleration of the car is

What is the magnitude of the acceleration of the car?

Questions 7-8

（含图）

A car moves in a straight line along the x-axis.

The velocity of the car v_x as a function of time t is shown in the graph above. The position x of the car at t = 0 is x = 0.

The average acceleration a_x of the car during the interval of 0 to 10 s is most nearly

The average velocity of the car during the interval of 0 to 10 s is most nearly

（含图）

Two blocks rest on a table, as shown above. The bottom block is pulled to the right by an applied force $$\vec{F}$$ that is strong enough so that the two blocks do not move together (i.e., they do not have the same acceleration or velocity). There is friction between the blocks, but the tabletop is frictionless. When the top block leaves the bottom block, where does it land and why?

A sphere of mass $$m$$ is dropped from the top of a building and reaches the ground before achieving terminal velocity. The force of air resistance that acts on the sphere as it falls is given by $$F = -kv$$, where $$k$$ is a positive constant and $$v$$ is the velocity of the sphere. What happens to the magnitude of the sphere's velocity and acceleration, and to the distance it falls during each second, as the sphere approaches the ground?

（含图）

Questions 11-12

An object of mass 0.5 kg is given an initial velocity and then slides across a horizontal surface. The object experiences a resistive force that is a function of velocity. The velocity v of the object as a function of time t is given by （含图）, where α = 2 m/s and β = 3 s⁻¹ .

Which of the following is a correct expression for the net force, in newtons, exerted on the object as a function of time?

The energy dissipated due to the resistive force after a very long time is most nearly

Questions 13-14

（含图）

Cart A is traveling east when it collides with cart B, which is traveling north. Cart A has a mass of 3.05 kg, and cart B has a mass of 2.10 kg. The two carts travel together as a single object on a horizontal surface at an angle θ relative to due east, as shown above.

In one trial, the initial speed of cart A is 2.5 m/s and the initial speed of cart B is 1.5 m/s. The angle θ relative to east that the carts travel after the collision is most nearly

In another trial, the speed of the carts immediately after the collision is 0.60 m/s, and the carts slide 0.24 m on the horizontal surface before coming to rest. The coefficient of kinetic friction between the sliding carts and the surface is most nearly

Questions 15-17

（含图）

A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k.

The coefficient of kinetic friction between the surface and the block is m. When the block is at position x = 0, the spring is at its unstretched length. The block is pulled to position x = +x₀ , as shown above, and released from rest. The block then travels to the left and passes through x = 0 before coming momentarily to rest at position x = - x₀/2 .

Which of the following is a correct expression for the kinetic energy of the block as it first travels through position $$x = 0$$?

Which of the following is a correct expression for the coefficient of kinetic friction $$\mu$$?

Which of the following is a differential equation that could be used to solve for the block's position $$x$$ as a function of time $$t$$ when it is moving to the left?

Questions 18-19

（含图）

In the diagram above, a block of mass M is initially at rest on a horizontal surface at the base of an inclined plane. The surface and plane have negligible friction. The block is struck by a projectile of mass m traveling with a horizontal velocity v_i. The projectile becomes embedded in the block, and they move together to the right with speed v_f.

Which of the following is a correct expression for v_f?

The block and projectile smoothly transition onto the inclined plane. Which of the following is a correct expression for the maximum height that the block moves up the inclined plane in terms of $$v_f$$?

The net force $$F$$ acting on an object that moves along a straight line is given as a function of time $$t$$ by $$F(t) = kt^2 + \tau$$, where $$k = 1\ \text{N/s}^2$$ and $$\tau = 1\ \text{N}$$. What is the change in momentum of the object from $$t = 0\ \text{s}$$ to $$t = 3\ \text{s}$$?

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