Question

ap physics c @ fhs - unit 2, kinematics: test v1 name: lucy luo date: 9/24 multiple choice: no calculators, no equation sheets. 1. if l represents the dimensions of length and t that of time, then the dimensions of acceleration are (a) l+t (b) l/t² (c) t/l (d) l/t (e) none of these 2. in the absence of air friction, an object dropped near the surface of the earth experiences a constant acceleration of about 9.8 m/s². this means that the (a) speed of the object increases 9.8 m/s during each second (b) speed of the object as it falls is 9.8 m/s (c) object falls 9.8 meters during each second (d) object falls 9.8 meters during the first second only (e) derivative of the distance with respect to time for the object equals 9.8 m/s² 3. the graph above shows the velocity v as a function of time t for an object moving in a straight line. which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval? questions 4 - 5 at time t = 0, car x traveling with speed v₀ passes car y, which is just starting to move. both cars then travel on two parallel lanes of the same straight road. the graphs of speed v versus time t for both cars are shown above. 4. which of the following is true at time t = 20 seconds? (a) car y is behind car x. (b) car y is passing car x. (c) car y is in front of car x. (d) both cars have the same acceleration. (e) car x is accelerating faster then car y. 5. from time t = 0 to time t = 40 seconds, the areas under both curves are equal. therefore, which of the following is true at time t = 40 seconds? (a) car y is behind car x. (b) car y is passing car x. (c) car y is in front of car x. (d) both cars have the same acceleration. (e) car x is accelerating faster than car y.

Explanation:

Step1: Recall acceleration - dimension relation

Acceleration $a=\frac{\Delta v}{\Delta t}$, where velocity $v = \frac{\Delta x}{\Delta t}$ and $x$ is displacement with dimension of length $[L]$ and $t$ is time with dimension of $[T]$. So $v$ has dimension $[L/T]$, and $a$ has dimension $\frac{[L/T]}{[T]}=[L/T^{2}]$. So the answer to the first - question is B.

Step2: Understand the meaning of $g = 9.8\ m/s^{2}$

Acceleration is the rate of change of velocity. An acceleration of $9.8\ m/s^{2}$ means the speed of the object increases by $9.8\ m/s$ each second. The answer to the second - question is B.

Step3: Relate velocity - time graph to displacement - time graph

The displacement $x$ is the integral of velocity $v$ with respect to time $t$. When $v$ is constant, $x$ changes linearly. When $v$ is increasing, $x$ is a concave - up curve, and when $v$ is decreasing, $x$ is a concave - down curve. The correct displacement - time graph is A.

Step4: Analyze the position of cars from $v - t$ graph

The displacement of an object is given by the area under the $v - t$ graph. At $t = 20\ s$, the area under the $v - t$ graph for car X is larger than that for car Y. So car Y is behind car X. The answer is A.

Step5: Analyze the position of cars at $t = 40\ s$

Since the areas under both curves are equal from $t = 0$ to $t = 40\ s$, the displacements of the two cars are equal at $t = 40\ s$, which means car Y is passing car X. The answer is B.

Answer:

1. B. $[L/T^{2}]$
2. B. speed of the object increases 9.8 m/s during each second
3. A.
4. A. Car Y is behind car X.
5. B. Car Y is passing car X.