11.2.A.1–2Multiple Choice
Which property DOES the object model keep, rather than discard, when treating an extended object as a single point?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 1.2 — the object model and displacement, average velocity and average acceleration, what it means for an object to be accelerating and how instantaneous values arise as a limit, instantaneous velocity as a derivative, and instantaneous acceleration together with recovering functions by differentiation and integration. Round decimals to the nearest tenth unless noted otherwise.
Which property DOES the object model keep, rather than discard, when treating an extended object as a single point?
Select A, B, C, or D to check your answer.
A particle moves from x₀ = 5 m to xf = −2 m. (a) Find its displacement Δx, including its sign. (b) State which direction it moved, taking rightward as positive.
A hiker walks from x = 0 m to x = 15 m, then back to x = 6 m. Which statement correctly compares the hiker's total distance and net displacement for the whole trip?
Select A, B, C, or D to check your answer.
Explain, using the object model, why a spinning basketball and a sliding hockey puck of the same mass can be treated identically in a kinematics problem, even though they look nothing alike.
A car travels from x₀ = 0 m to x_f = 150 m in 10 s. What is its average velocity?
Select A, B, C, or D to check your answer.
A car's velocity changes from +10 m/s to +2 m/s over 4 s as the driver brakes. (a) Find the car's average acceleration. (b) Explain what the sign of your answer tells you about the car's motion.
An object's velocity changes from −6 m/s to −2 m/s over 2 s. What is its average acceleration?
Select A, B, C, or D to check your answer.
An object moves +50 m in the first 10 s, then −20 m in the next 5 s. (a) Find its average velocity for the entire trip. (b) A classmate instead averages the two legs' individual average velocities (+5 m/s and −4 m/s) to get 0.5 m/s. Explain why that approach is wrong.
A car travels around a circular track at a constant speed of 20 m/s. Is the car accelerating?
Select A, B, C, or D to check your answer.
An elevator moves upward at a constant 2 m/s for 5 s, then slows smoothly to rest over the next 3 s. Identify during which part(s) of this motion the elevator is accelerating, and explain your reasoning for each part.
For x(t) = t² (meters), the average velocity over the interval [2 s, 2.1 s] works out to 4.1 m/s. As the interval is shrunk further and further toward zero, this average velocity approaches which value?
Select A, B, C, or D to check your answer.
Explain why calculating an average acceleration over a very small time interval gives a value close to the instantaneous acceleration, but calculating it over a large time interval might not.
A particle's position is given by x(t) = 5t² (meters). What is its instantaneous velocity at t = 3 s?
Select A, B, C, or D to check your answer.
A particle's position is x(t) = 4t³ − 6t (meters). (a) Find v_x(t). (b) Evaluate v_x at t = 2 s.
Instantaneous velocity is defined as...
Select A, B, C, or D to check your answer.
A position function x(t) is a straight line for the first 4 s, then curves increasingly steeply upward afterward. Explain what this tells you about the object's instantaneous velocity during each portion, and why the shapes differ.
A particle's velocity is v_x(t) = 8t − 3 (m/s). Which expression gives its instantaneous acceleration a_x(t)?
Select A, B, C, or D to check your answer.
A particle has constant acceleration a_x = 6 m/s², and its velocity at t = 0 is v₀ = 2 m/s. (a) Integrate to find v_x(t). (b) Evaluate v_x at t = 3 s.
A particle's position is x(t) = 2t³ − 5t (meters). Which expression gives its instantaneous acceleration a_x(t)?
Select A, B, C, or D to check your answer.
A particle's position is x(t) = t³ − 3t² (meters). (a) Find v_x(t). (b) Find a_x(t). (c) Evaluate both at t = 1 s, and state whether the particle is accelerating at that instant.