t = time d = distance
Alana walking rate: 1 meter per second
Gilberto walking rate: 2 meters per second
Leanne walking rate: 2.5 rating per second
Alana Equation: d = t
Gilberto Equation: d = 2t
Leanne Equation: d = 2.5t
I made a table for the first ten seconds of each of the students, and then a graph. What does it mean when it says "If t increases by 1 second, by how much does the distance change? How is this change represented in a change? In a graph?"
What does it mean by "if t increases by 1 second, by how much does the distance change?" How can t increase?
Then it says the same thing, but for 5 seconds, and the question after that says "What is the walking rate per minute? The walking rate per hour?
at 3 m/s,
time t: 3t
time t+1: 3(t+1) = 3t+3
"When it says 'if t increases by 1 second, by how much does the distance change?', it is referring to what happens to the distance traveled when the time, t, is incremented by 1 second. In this scenario, t represents the time in seconds. By increasing t by 1 second, you are essentially asking, 'If an additional second is added to the time, how much does the distance change?'
To calculate this change for each student, you can use their respective equations. Considering Alana's equation d = t, if you increase t by 1 second, the distance would increase by 1 meter, as her walking rate is 1 meter per second.
Now, for Gilberto's equation d = 2t, when t increases by 1 second, the distance would increase by 2 meters. This is because his walking rate is 2 meters per second.
Similarly, for Leanne's equation d = 2.5t, when t increases by 1 second, the distance would increase by 2.5 meters. The equation reflects her walking rate of 2.5 meters per second.
To represent this change in a graph, you can plot the time, t, on the x-axis and the distance, d, on the y-axis. Each point on the graph would represent a specific time and distance pair. By connecting these points, you can observe the pattern and visualize the change in distance over time for each student.
Now, moving on to the second question regarding a time increment of 5 seconds: If you increase t by 5 seconds instead of 1, you can apply the same reasoning to find out the change in distance for each student. Just multiply the walking rate of each student by 5 to determine the change in distance.
For the walking rate per minute, you can multiply the walking rate per second by 60 (since there are 60 seconds in a minute). Similarly, for the walking rate per hour, multiply the walking rate per second by 3,600 (since there are 3,600 seconds in an hour). This will give you the distance traveled in one minute or one hour for each student."