Question

section 2.4

1. rank the four points on the position vs. time graph in order from slowest to fastest.
2. draw the position vs. time graph for a person walking at a constant speed of 1 m/sec for 10 seconds. on the same axes, draw the graph for a person running at a constant speed of 4 m/sec.
3. calculate speed from the position vs. time graph to the right. show your work.
4. draw the position vs. time graph for an object that is not moving.
5. why is the position vs. time graph for an object in free - fall a curve?
6. draw the speed vs. time graph showing the same motion as the position vs. time graph to the right.
7. draw a speed vs. time graph for a car that starts at rest and steadily accelerates until it is moving at 40 m/sec after 20 seconds. then calculate the car’s acceleration and the distance it traveled during the 20 seconds.
8. draw a speed vs. time graph for an object accelerating from rest at 2 m/sec².

Explanation:

Step1: Recall speed - slope relationship

Speed on a position - time graph is given by the slope of the graph. The steeper the slope, the faster the speed.

Step2: Analyze the slopes of points on first graph

For the first graph with four points, we observe the slopes at each point. Point 3 has the flattest slope, followed by point 4, then point 1, and point 2 has the steepest slope.

for question 12:
The position - time graph for a constant - speed motion is a straight line. The equation for position $x = vt$, where $v$ is the speed and $t$ is the time. For a person walking at $v_1=1$ m/s for 10 s, the position $x_1 = 1\times t$ (a line with slope 1). For a person running at $v_2 = 4$ m/s, the position $x_2=4\times t$ (a line with slope 4).

for question 13:
The speed $v$ on a position - time graph is calculated as $v=\frac{\Delta x}{\Delta t}$. For the given position - time graph, if we take two points $(t_1,x_1)$ and $(t_2,x_2)$ on the line, say $(0,1)$ and $(4,3)$, then $\Delta x=x_2 - x_1=3 - 1 = 2$ m and $\Delta t=t_2 - t_1=4 - 0 = 4$ s. So $v=\frac{2}{4}=0.5$ m/s.

for question 14:
If an object is not moving, its position does not change with time. So the position - time graph is a horizontal line.

Answer:

3, 4, 1, 2