Question

for questions 9 through 11, refer to the graph below. distance - time graph distance (meters) 0 100 200 300 400 0 2 4 6 8 10 time (seconds) 9. draw a point on the graph that represents 200 m traveled in 4 seconds. draw a line connecting this point with the origin (0,0). label this as line a. 10. draw a point on the graph that represents 100 m traveled in 10 seconds. draw a line connecting this point with the origin (0,0). label this as line b. 11. calculate the average speed (slope) of lines a and b. be sure to include units. velocity (page 336) 12. how do speed and velocity differ? 13. circle the letter of each sentence that describes a change in velocity. a. a moving object gains speed. b. a moving object changes direction. c. a moving object moves in a straight line at a constant speed. d. a moving object slows down. 14. is the following sentence true or false? if a car travels around a gentle curve on a highway at 60 km/h, the velocity does not change. combining velocities (page 337) 15. how do velocities combine? 16. a river flows at a velocity of 3 km/h relative to the riverbank. a boat moves upstream at a velocity of 15 km/h relative to the river. what is the velocity of the boat relative to the riverbank? a. 18 km/h downstream b. 15 km/h upstream c. 12 km/h upstream d. 12 km/h downstream

Explanation:

Step1: Calculate slope for line A

The slope (average - speed) formula is $m=\frac{\Delta y}{\Delta x}$. For line A, $\Delta y = 200$ m and $\Delta x=4$ s. So, $m_A=\frac{200\ m}{4\ s}=50$ m/s.

Step2: Calculate slope for line B

For line B, $\Delta y = 100$ m and $\Delta x = 10$ s. So, $m_B=\frac{100\ m}{10\ s}=10$ m/s.

Step3: Answer question 12

Speed is a scalar quantity (only magnitude), while velocity is a vector quantity (magnitude and direction).

Step4: Answer question 13

Velocity changes when there is a change in speed or direction. So, a, b, and d describe changes in velocity.

Step5: Answer question 14

If a car travels around a curve at a constant speed, its direction changes, so its velocity changes. The statement is false.

Step6: Answer question 15

Velocities combine according to vector - addition rules. If the velocities are in the same direction, add their magnitudes; if in opposite directions, subtract the magnitudes.

Step7: Answer question 16

The river flows downstream at 3 km/h and the boat moves upstream at 15 km/h relative to the river. The velocity of the boat relative to the riverbank is $v = 15 - 3=12$ km/h upstream.

Answer:

1. Line A: 50 m/s; Line B: 10 m/s
2. Speed is scalar, velocity is vector (magnitude and direction).
3. a, b, d
4. False
5. According to vector - addition rules.
6. c. 12 km/h upstream