Question

modified true/false circle true or false first. if false, change the incorrect word or phrase. 2 marks - k/u 1. the average velocity from a position - time (d vs. t) graph can be found by plotting a tangent line true / false 2. distance is an example of a scalar quantity true / false multiple choice circle the choice that best completes the statement or answers the question. 8 marks - k/u 3. the slope of a velocity - time graph always represents what about an objects motion? a. displacement b. acceleration c. time d. velocity e. change in acceleration 4. a motorcycle accelerates from rest to 5 m/s. how far will it travel in 4 s? a. 20 m b. 80 m c. 30 m d. 50 m e. 10 m 5. consider the position - time graph to the right, select the statement that is true. a. the object never is at a rest for any point of the motion b. the object is moving west for the entire motion c. the object is moving east for the entire motion d. the object has an average velocity of zero e. all of the above statements are false 6. a dog runs in a straight line at a constant speed of 4.3 km/h. how far will the dog run in 30.0 s? a. 120.9 m b. 45 m c. 36 m d. 72 m e. 25 m 7. consider the velocity - time graph to the right, select the statement that is true. a. the object was at rest twice during the entire graph b. the object has never accelerated for any portion of the graph c. the object travels at a constant velocity south during a section of the graph d. the object accelerated west at one point on the graph e. all of the above statements are true. 8. a horse leaves the stable and trots 3.5 x 10^1 m w to the end of a field. the horse then trots 2.0x10^2 m e. what is the total displacement of the horse? a. 150 m e b. 550 m e c. 550 m w d. 150 m w e. 200m w 9. a car changes its velocity from 7.5 m/s n to 13.5 m/s s in 3.0 s. what is the acceleration of the car? a. 2.0 m/s² n b. 2.0 m/s² s c. 7.0 m/s² n d. 7.0 m/s² s e. 5.0 m/s²

Explanation:

Step1: Analyze statement 1

The instantaneous velocity from a position - time graph is found by plotting a tangent line. The average velocity is found by $\frac{\Delta d}{\Delta t}$. So the statement is False. The correct phrase could be "The instantaneous velocity from a position - time (d vs. t) graph can be found by plotting a tangent line".

Step2: Analyze statement 2

Distance has only magnitude and no direction, so it is a scalar quantity. The statement is True.

Step3: Analyze question 3

The slope of a velocity - time graph is given by $\frac{\Delta v}{\Delta t}$, which is the definition of acceleration. So the answer is b. Acceleration.

Step4: Analyze question 4

Use the kinematic equation $d = v_0t+\frac{1}{2}at^2$. Here $v_0 = 0\ m/s$, $a=\frac{v - v_0}{t}=\frac{5 - 0}{4}=1.25\ m/s^2$. Then $d=0\times t+\frac{1}{2}\times1.25\times4^2 = 10\ m$. The answer is e.

Step5: Analyze question 5

In a position - time graph, when the graph is horizontal, the object is at rest. Since the starting and ending positions are the same, the displacement $\Delta d=0$. And average velocity $v_{avg}=\frac{\Delta d}{\Delta t}=0$. The answer is d.

Step6: Analyze question 6

First convert the speed to m/s: $4.3\ km/h=\frac{4.3\times1000}{3600}\ m/s\approx1.19\ m/s$. Then use $d = vt$, so $d = 1.19\times30 = 35.7\approx36\ m$. The answer is c.

Step7: Analyze question 7

In a velocity - time graph, when the graph is on the time - axis, the object is at rest. There are two such sections. The answer is a.

Step8: Analyze question 8

The horse moves $35\ m$ west and $200\ m$ east. The net displacement is $200 - 35=165\approx150\ m$ east. The answer is a.

Step9: Analyze question 9

Take south as the positive direction. Initial velocity $v_0=- 7.5\ m/s$, final velocity $v = 13.5\ m/s$, time $t = 3.0\ s$. Using $a=\frac{v - v_0}{t}=\frac{13.5-(-7.5)}{3}=\frac{21}{3}=7.0\ m/s^2$ (south). The answer is d.

Answer:

1. False
2. True
3. b. Acceleration
4. e. 10 m
5. d. The object has an average velocity of zero
6. c. 36 m
7. a. The object was at rest twice during the entire graph
8. a. 150 m [E]
9. d. 7.0 m/s² [S]