APP1 - 1.3 APC

A cart moves along a horizontal, one-dimensional track according to the position-time graph shown, where positive position values represent locations to the right of the origin. Which of the following statements correctly describe the cart’s instantaneous velocity at time 5 s?

• The cart is moving left with speed 1.0 cm/s.

• The cart is moving right with speed 1.0 cm/s.

• The cart is moving left with speed 0.5 cm/s.

• The cart is moving right with speed 0.5 cm/s.

Answer explanation

At time 5 s, the position-time graph shows a negative slope, indicating the cart is moving left. The slope is -1.0 cm/s, confirming the cart's speed is 1.0 cm/s to the left.

Which of the following is an expression for the time it takes for Car B to catch up to Car A, given that Car A travels at constant velocity v_A and Car B starts from rest with constant acceleration a_B at t = 0?

• (2v_A)/(a_B)

• (v_A)/(a_B)

• It cannot be determined without knowing the distance traveled by the cars.

Answer explanation

To find the time it takes for Car B to catch Car A, we set the distance equations equal. Car A travels at v_A * t, while Car B travels (1/2) * a_B * t^2. Setting these equal and solving gives t_f = v_A / a_B.

The graphs represent the speed of a ball thrown downward as a function of time near the surface of two planets. Which of the following correctly relates the acceleration a_1 of the ball near the surface of Planet 1 and the acceleration a_2 of the ball near the surface of Planet 2?

• a_1 > a_2 > 0

• a_2 > a_1 > 0

• (a_1 = a_2) > 0

• a_1 = a_2 = 0

Answer explanation

The acceleration of a ball thrown downward is influenced by the gravitational pull of the planet. If the graph for Planet 1 shows a steeper slope than for Planet 2, it indicates a greater acceleration. Thus, a_1 > a_2 > 0.

• The car moves with constant speed, momentarily stops, and then moves again with the same speed

• The car is speeding up at a constant rate, then continues to speed up but at a slower constant rate

• The car moves with constant speed, then it quickly slows down to a different, constant speed

• The car is speeding up at a constant rate, then slows down at a constant rate

Answer explanation

The graph shows position as a function of t^2, indicating a quadratic relationship. This means the car's velocity is changing at a constant rate, which defines constant acceleration.

A car is moving with constant speed v₀ when a tree falls into the roadway at t = 0. It takes the driver a time T to react and apply the brakes. The car then slows with a constant acceleration of magnitude a. Which of the following equations correctly expresses the distance D traveled by the car from time t = 0 to the instant the car comes to rest?

• D = v₀T + (1/2)aT²

• D = (1/2)aT² + v₀²/2a

• D = v₀T + v₀²/2a

• D = v₀T + (1/2)aT² + v₀²/2a

Answer explanation

The car travels distance D during the reaction time T at speed v₀, plus the distance it travels while decelerating to rest. The correct equation is D = v₀T + v₀²/2a, which accounts for both phases of motion.

A car on a straight track is at position xᵢ and has initial speed vᵢ when it begins to slow down with constant acceleration of magnitude a. When the car reaches position x_f it has speed v_f. Which of the following is a correct expression for x_f?

• (v_f² - vᵢ²)/2a + xᵢ

• (vᵢ² - v_f²)/2a + xᵢ

• (v_f² - vᵢ²)/2a - xᵢ

• (vᵢ² - v_f²)/2a - xᵢ

Answer explanation

The correct expression for the final position x_f is derived from the kinematic equation: x_f = x_i + (v_f² - vᵢ²) / (2a). Thus, the correct choice is (v_f² - vᵢ²)/2a + xᵢ.

An object is dropped from a tall building at time t = 0 s and reaches the ground at t = 10 s. Which of the following correctly compares the distance traveled by the object between different time intervals?

• Δx₀₋₂ > Δx₄₋₆ > Δx₈₋₁₀

• Δx₀₋₂ = Δx₄₋₆ = Δx₈₋₁₀

• Δx₈₋₁₀ > Δx₄₋₆ > Δx₀₋₂

• (Δx₀₋₂ = Δx₈₋₁₀) > Δx₄₋₆

Answer explanation

As the object falls, it accelerates due to gravity. Thus, the distance traveled in later intervals (Δx₈₋₁₀) is greater than in earlier intervals (Δx₀₋₂ and Δx₄₋₆). Therefore, Δx₈₋₁₀ > Δx₄₋₆ > Δx₀₋₂ is correct.

The graph shows the position x of an object as a function of time t as it moves along the x-axis. Which of the following claims about the motion of the object during the time interval shown is correct?

• The object is moving with constant speed in the −x-direction.

• The object is moving with constant speed in the +x-direction.

• The velocity and acceleration are both in the −x-direction.

• The velocity is in the +x-direction and the acceleration is in the −x-direction.

Answer explanation

The graph indicates that the position x decreases over time, showing the object is moving in the −x-direction. Since the position is changing consistently, both velocity and acceleration are also in the −x-direction.

A cart starts from rest and moves to the right along a flat surface. The velocity of the cart as a function of time is represented in the graph. Which of the following quantities are the same for both segment A and segment B of the graph?

• Acceleration

• Displacement

• Elapsed time

• Average velocity

Answer explanation

The change in velocity is the same for both segments A and B, as it is determined by the initial and final velocities. Average velocity, time interval, and acceleration may differ between segments.