Question

1. use your understanding of the meaning of slope and shape of position - time graphs to describe the motion depicted by each of the following graphs.
2. use the position - time graphs below to determine the velocity. psyw

Explanation:

Step1: Recall velocity - position - time relation

Velocity $v$ is given by the slope of the position - time graph, $v=\frac{\Delta x}{\Delta t}$.

Step2: For the first graph in part 5

Pick two points, say $(0,0)$ and $(5, 20)$. Then $\Delta x = 20 - 0=20$ m and $\Delta t=5 - 0 = 5$ s. So $v=\frac{20}{5}=4$ m/s.

Step3: For the second graph in part 5

Pick two points, e.g., $(0,5)$ and $(5,20)$. $\Delta x=20 - 5 = 15$ m and $\Delta t = 5-0=5$ s. So $v=\frac{15}{5}=3$ m/s.

Step4: For the third graph in part 5

Pick two points, like $(0,25)$ and $(5,0)$. $\Delta x=0 - 25=- 25$ m and $\Delta t=5 - 0 = 5$ s. So $v=\frac{-25}{5}=-5$ m/s.

Step5: For the fourth graph in part 5

Pick two points, such as $(0,25)$ and $(5,10)$. $\Delta x=10 - 25=-15$ m and $\Delta t=5 - 0 = 5$ s. So $v=\frac{-15}{5}=-3$ m/s.

For the verbal - description part in question 4:

• First non - horizontal graph in question 4 (left - top): The object is moving with a constant negative velocity (since the slope is negative and constant).
• Second non - horizontal graph in question 4 (right - top): The object is moving with a constant negative velocity and has a negative acceleration (the slope is negative and the position is decreasing at a constant rate).
• First graph in the middle row of question 4 (left): The object is initially moving slowly (small positive slope), then speeds up (positive acceleration as the slope increases).
• Second graph in the middle row of question 4 (right): The object is moving with a positive velocity and slows down (negative acceleration) as the slope decreases towards zero.
• First graph in the bottom row of question 4 (left): The object is initially at rest (zero slope), then starts moving with a positive velocity (positive acceleration as the slope becomes non - zero and positive).
• Second graph in the bottom row of question 4 (right): The object is moving with a positive velocity and then comes to rest (negative acceleration as the slope decreases to zero).

Answer:

For part 5:
First graph: $4$ m/s
Second graph: $3$ m/s
Third graph: $-5$ m/s
Fourth graph: $-3$ m/s