Question

activity a: velocity - time graphs
get the gizmo ready:

• click the red reset button on the stopwatch.
• change the number of points to 5.
• turn off show graph and show animation for runner 2.

speed is a measure of how fast an object moves, regardless of direction. speed can never be negative. velocity describes both speed and direction, and can be positive or negative.

1. in the gizmo, make a position - time graph for runner 1 with the following features:

• there is at least one major change in speed.
• there is at least one major change in direction.

click the green start button and watch the runner run. adjust your graph if needed to meet the requirements.
sketch your graph to the right.

1. where was the runner each second? based on your graph, fill in all except the final column in the table below. (leave the velocity column blank for now.) label any numbers with units.

time	position at end of time interval (yds)	distance moved this time interval (yds)	to the left or right?	velocity this time interval (y/s)
0 - 1 sec
1 - 2 sec
2 - 3 sec
3 - 4 sec

1. to calculate the velocity for each time interval, first calculate the speed of the runner in that interval (speed = distance + time). if the direction is left to right, velocity is positive. if the direction is right to left, velocity is negative.

fill in the velocity column of the table above. use units (y/s).
when this runner is running to the left (negative velocity), what does his position - time graph look like?

Explanation:

Step1: Sketch the position - time graph

To meet the requirements of at least one major change in speed and direction for Runner 1 in the Gizmo, we can start with the runner moving to the right with a certain speed for the first second (a positive - sloped line on the position - time graph), then stop for a short time (a horizontal line), and then move to the left (a negative - sloped line).

Step2: Determine position at each time interval

For the 0 - 1 sec interval, assume the runner starts at 0 yds and moves to the right 10 yds. So the position at the end of 0 - 1 sec is 10 yds, distance moved is 10 yds, and direction is to the right.
For the 1 - 2 sec interval, assume the runner stops. So the position at the end is still 10 yds, distance moved is 0 yds, and direction is none.
For the 2 - 3 sec interval, assume the runner moves to the left 5 yds. So the position at the end is 5 yds, distance moved is 5 yds, and direction is to the left.
For the 3 - 4 sec interval, assume the runner moves to the left another 5 yds. So the position at the end is 0 yds, distance moved is 5 yds, and direction is to the left.

Step3: Calculate velocity

For the 0 - 1 sec interval: speed = distance/time = 10 yds/1 s=10 y/s, direction is right so velocity is 10 y/s.
For the 1 - 2 sec interval: speed = 0 yds/1 s = 0 y/s, velocity is 0 y/s.
For the 2 - 3 sec interval: speed = 5 yds/1 s = 5 y/s, direction is left so velocity is - 5 y/s.
For the 3 - 4 sec interval: speed = 5 yds/1 s = 5 y/s, direction is left so velocity is - 5 y/s.
When the runner is running to the left (negative velocity), the position - time graph has a negative slope, meaning the position of the runner decreases as time increases.

Time	Position at end of time interval (yds)	Distance moved this time interval (yds)	To the left or right?	Velocity this time interval (y/s)
1 - 2 sec	10	0	None	0
2 - 3 sec	5	5	Left	- 5
3 - 4 sec	0	5	Left	- 5

Answer:

The position - time graph for a runner with negative velocity (running to the left) has a negative slope, indicating that the position of the runner decreases as time progresses. The table above shows the position, distance moved, direction, and velocity for each time interval.