Representing Motion AP Physics C Mechanics MCQ – Exam Style Questions etc.
Representing Motion AP Physics C Mechanics MCQ
Unit: 1. Kinematics
Weightage : 10-15%
Question
An object moves along a straight line with a velocity v given as a function of time t by the equation \(v(t)=\alpha t^2+\beta t+\gamma \)
Which of the following expressions represents a (t ) , the acceleration of the object as a function of time t ?
(A)\(2\alpha\)
(B)\(\alpha t+\beta\)
(C)\(2\alpha t+\beta\)
(D)\(\alpha t^3/3+\beta t^2/2+\gamma t\)
(E)\(3\alpha t^3+2\beta t^2+\gamma t\)
Answer/Explanation
Ans:C
Question
A cart is moving in the +x-direction and passes the origin when time t= 0. The cart then moves with decreasing speed, stops, and moves in the –x-direction with increasing speed. Which of the following graphs best represents the cart’s position x as a function of time?
Answer/Explanation
Ans:A
Questions(a)-(b)
A car moves in a straight line along the x-axis. The velocity of the car vx as a function of time t is shown in the graph above. The position x of the car at t = 0 is x = 0.
Question(a)
The average acceleration \(a_x\) of the car during the interval of 0 to 10 s is most nearly
(A) \( −2.0 m/ s^2\)
(B) \(−0.40 m/ s^2\)
(C)\(+ 0.40 m/ s^2\)
(D) \( +1.0 m/ s^2\)
(E)\(+2.0 m/ s^2\)
Answer/Explanation
Ans:B
The average acceleration is the average rate of velocity change over a time interval. For a velocity-time graph, that will be the slope of the straight line connecting the starting and ending
points. Solving for the slope yields
\(a_{avg}=slope=\frac{(2m/s)-6m/s}{(10s-0s)}=0.40m/s^2\).
Question(b)
The average velocity of the car during the interval of 0 to 10 s is most nearly
(A) −1.4 m/ s
(B) +0.40 m/ s
(C) +1.4 m/ s
(D) +1.8 m/ s
(E)+4.0 m /s
Answer/Explanation
Ans:B
By definition, the average velocity is the average rate of position change over an interval. Mathematically, this is \(\frac{\Delta x}{\Delta t}\).Therefore, using the velocity graph’s Δx value, which is the sum of the signed areas under the curve,
