### Extended Response

### 2.1 Relative Motion, Distance, and Displacement

Find the distance traveled from the starting point for each path.

Which path has the maximum distance?

- The distance for Path A is 6 m, Path B is 4 m, Path C is 12 m and for Path D is 7 m. The net displacement for Path A is 7 m, Path B is â€“4m, Path C is 8 m and for Path D is â€“5m. Path C has maximum distance and it is equal to 12 meters.
- The distance for Path A is 6 m, Path B is 4 m, Path C is 8 m and for Path D is 7 m. The net displacement for Path A is 6 m, Path B is â€“4m, Path C is 12 m and for Path D is â€“5 m. Path A has maximum distance and it is equal to 6 meters.
- The distance for Path A is 6 m, Path B is 4 m, Path C is 12 m and for Path D is 7 m. The net displacement for Path A is 6 m, Path B is â€“4 m, Path C is 8 m and for Path D is â€“5 m. Path C has maximum distance and it is equal to 12 meters.
- The distance for Path A is 6 m, Path B is â€“4 m, Path C is 12 m and for Path D is â€“5 m. The net displacement for Path A is 7 m, Path B is 4 m, Path C is 8 m and for Path D is 7 m. Path A has maximum distance and it is equal to 6 m.

- Displacement is 0 km and distance is 7 km.
- Displacement is 0 km and distance is 3.5 km.
- Displacement is 7 km towards west and distance is 7 km.
- Displacement is 3.5 km towards east and distance is 3.5 km.

### 2.2 Speed and Velocity

- Runner A will be $72\xc3\u2014{10}^{3}$ m away and Runner B will be $59.5\xc3\u2014{10}^{3}$ m away from the starting point.
- Runner A will be $1.2\xc3\u2014{10}^{2}$ m away and runner B will be $1.1\xc3\u2014{10}^{2}$ m away from the starting point.
- Runner A will be $1.2\xc3\u2014{10}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{m}$ away and Runner B will be $1.3\xc3\u2014{10}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{m}$ away from the starting point.
- Runner A will be $7.2\xc3\u2014{10}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{m}$ away and Runner B will be $1.3\xc3\u2014{10}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{m}$ away from the starting point.

A father and his daughter go to the bus stop that is located 75 m from their front door. The father walks in a straight line while his daughter runs along a varied path. Despite the different paths, they both end up at the bus stop at the same time. The fatherâ€™s average speed is 2.2 m/s, and his daughterâ€™s average speed is 3.5 m/s. (a) How long does it take the father and daughter to reach the bus stop? (b) What was the daughterâ€™s total distance traveled? (c) If the daughter maintained her same average speed and traveled in a straight line like her father, how far beyond the bus stop would she have traveled?

- (a) 21.43 s (b) 75 m (c) 0 m
- (a) 21.43 s (b) 119 m (c) 44 m
- (a) 34 s (b) 75 m (c) 0 m
- (a) 34 s (b) 119 m (c) 44 m

### 2.3 Position vs. Time Graphs

What kind of motion would create a position graph like the one shown?

- uniform motion
- any motion that accelerates
- motion that stops and then starts
- motion that has constant velocity

What is the average velocity for the whole time period shown in the graph?

- $\xe2\u20ac\u201c\frac{1}{3}\text{m/s}$
- $\xe2\u20ac\u201c\frac{3}{4}\text{m/s}$
- $\frac{1}{3}\text{m/s}$
- $\frac{3}{4}\text{m/s}$

### 2.4 Velocity vs. Time Graphs

Consider the motion of the object whose velocity is charted in the graph.

During which points is the object slowing down and speeding up?

- It is slowing down between
*d*and*e*. It is speeding up between*a*and*d*and*e*and*h* - It is slowing down between
*a*and*d*and*e*and*h*. It is speeding up between*d*and*e*and then after*i*. - It is slowing down between
*d*and*e*and then after*h*. It is speeding up between*a*and*d*and*e*and*h*. - It is slowing down between
*a*and*d*and*e*and*h*. It is speeding up between*d*and*e*and then after*i*.

Divide the graph into approximate sections, and use those sections to graph the velocity vs. time of the object.

Then calculate the acceleration during each section, and calculate the approximate average velocity.

- Acceleration is zero and average velocity is 1.25 m/s.
- Acceleration is constant with some positive value and average velocity is 1.25 m/s.
- Acceleration is zero and average velocity is 0.25 m/s.
- Acceleration is constant with some positive value and average velocity is 0.25 m/s.