Displacement, Velocity, and Acceleration AP Physics C Mechanics MCQ – Exam Style Questions etc.
Displacement, Velocity, and Acceleration AP Physics C Mechanics MCQ
Unit: 1. Kinematics
Weightage : 10-15%
Question
Persons X, Y, and Z walk along a circular path of radius 50 m. Person X walks halfway around the path, Person Y walks \(3/4\) of the way around the path, and Person Z walks completely around the path. Which of the following correctly lists the walkers in order of the magnitudes of their displacement vectors from the least to the greatest?
A \(X < Y < Z\)
B \(X < Z < Y\)
C \(Y < X < Z\)
D \(Y < Z < X\)
E \(Z < Y < X\)
Answer/Explanation
Ans:E
Question
An object starts from rest at the origin of an xy-coordinate system and has an acceleration with components \(a_x=a\) and \(a_y=a\). After t seconds, the displacement and velocity of the object are \(Δd_1\) and \(v_1\), respectively. The object is stopped and returned to the origin. The object then starts at rest again with acceleration components \(a_x=2a\) and \(a_y=2a\). After t seconds, the displacement and velocity of the object are \(Δd_2\) and \(v_2\), respectively. Which of the following correctly relates \(Δd_1\) and \(v_1\) to \(Δd_2\) and \(v_2\) , respectively?
A \(Δd_2=4Δd_1\) and \(v_2=2v_1\)
B \(Δd_2=2Δd_1\) and \(v_2=\sqrt{2}v_1\)
C \(Δd_2=\sqrt{2}Δd_1\) and \(v_2=\sqrt{2}v_1\)
D \(Δd_2=\sqrt{5}Δd_1\) and \(v_2=\sqrt{5}v_1\)
E \(Δd_2=2Δd_1\) and v2=2v1
Answer/Explanation
Ans;E
Using vector addition for the acceleration, \(a_1=\sqrt{a^2+a^2}=\sqrt{2}a\) . Then, using kinematics equations,
Question
The following questions are related to this scenario:
The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and ω
are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all.
Which pair of equations can describe the path of a particle moving with an acceleration that is perpendicular to the velocity of the particle at t = 0 and remains constant in magnitude and direction?
A \(x=Acosωt\) , \(y=Asinωt\)
B \(x=Acosωt\) , \(y=2Acosωt\)
C \(x=At\) , y=\(Bt\)
D \(x=At^2\) , \(y=Bt^2\)
E \(x=At\) , \(y=Bt^2\)
Answer/Explanation
Ans:E
Question
The following questions are related to this scenario:
The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and ω
are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all.
Which pair of equations can describe the path of a particle moving with zero acceleration?
A \(x=Acosωt\) , \(y=Asinωt\)
B \(x=Acosωt\) , \(y=2Acosωt\)
C \(x=At\) , y=\(Bt\)
D \(x=At^2\) , \(y=Bt^2\)
E \(x=At\) , \(y=Bt^2\)
Answer/Explanation
Ans:C
Questions (a) and (b): A ball is thrown off a cliff, with an initial velocity directed at an angle \(\theta\) downward and to the right.
Question(a)
Which of the following is correct about the ball’s acceleration from when the ball is released until it hits the ground?
(A) It remains constant and is directed at the angle \(\theta\).
(B) It remains constant and is directed downward.
(C) It increases and its direction changes.
(D) It increases and is directed downward.
(E) It increases and is directed at the angle \(\theta\).
Answer/Explanation
Ans:B
Regardless of how it’s thrown, once released, the ball is in free-fall: no forces except gravity act on the ball. All objects in free-fall experience a constant acceleration of 10 m/s/s downward.