Week 04 · Linear Graphs and Rates of Change

Wednesday

Loft Lab: time the cart

// The cart on the ramp, one second at a time

⏱ about 20 min

Wednesday: Loft Lab, Time the Cart

Comet drags the sawhorses apart so the plank barely tilts. "Lab day. Gentle plank, five runs."

Wren hands her the stopwatch and a towel for the end of the ramp. "I release, you call the marks."

"Wait," Comet says. "Where do we start the clock?" She rushes to let go, then stops herself.

"At the release," Wren says. "Same start every time, or the readings will not line up."

Nova projects an empty table: seconds across the top, marks below. "Would you like a hint? Fill it as you go."

Run one: 1, 4, 7, 10, 13. Run two: 1, 4, 7, 10, 13 again. Comet grins. "Steady."

"Steady roll, steady line," Wren says. "Our engineer, run the lab, then compare your rate with ours."

What you need

A long plank or board on two low supports, tilted only a little, with a folded towel at the bottom.
A small toy cart or any small wheeled toy, and masking tape for marks every 10 centimeters.
A stopwatch or a phone timer, and a helper to call the marks while you keep time.
Your Loft Log, graph paper and a ruler.

Safety first

A grown-up sets up the plank and checks that the supports cannot tip. Keep feet and fingers clear of the rolling cart.
Keep the tilt gentle so the cart rolls, never flies. The towel at the end stops it.
Nothing is thrown or dropped from a height, and the cart stays on the plank.

Run the lab

Tape marks along the plank every 10 centimeters and number them from 0 at the top.
Hold the cart with its front wheels at mark 1. Start the timer the moment you let go.
Have your helper call out the mark the cart is passing at each second. Write every reading down.
Repeat for five runs from the same start. Keep the plank at the same tilt.
Plot seconds across and marks up, with labels and a scale. Lay a ruler along the dots.
Find your rate of change from two readings. Then compare it with the crew's rate of 3 marks a second.

The crew's lab log

Here are the crew's own readings for two runs on the gentle plank. Both are their made-up Loft data for this lesson.

Seconds	Run 1 (marks)	Run 2 (marks)	Run 2 (centimeters)
0	1	1	10
1	4	4	40
2	7	7	70
3	10	10	100
4	13	13	130

$A scatter plot of run 2 in centimeters, seconds across and centimeters up, with the points on one straight line.$

READ THE CREW'S RUNS

Read the question.
Tap your answer.

Run 1 went from mark 1 at 0 seconds to mark 13 at 4 seconds. What is the rate in marks per second?

In centimeters, run 2 passed 40 at 1 second and 130 at 4 seconds. What is the rate in centimeters per second?

Run 2 in centimeters went through (0, 10) and (4, 130). Which equation fits?

Run 2 follows d = 30t + 10 in centimeters. How many centimeters from the start line is the cart at 5 seconds? Type the number.

WHY THIS EXERCISEA rule lets you predict a reading you did not take, as long as the roll stays steady.

Statement	True or false?
Starting the timer at the same moment every run keeps the readings lined up.	?
A steeper plank would give a bigger rate of change.	?
The point (3, 100) is on the graph of y = 30t + 10.	?
The point (2, 60) is on the graph of y = 30t + 10.	?
130 - 40 = 30 × 3	?

WHY THIS EXERCISEA lab only gives a clean line when the setup is the same for every reading.

Try it

Lift one end of the plank a little higher and run the cart again. Does your line get steeper?
Keep the tilt gentle and the towel in place every time.

Draw your lab graph: seconds across, marks up, labels, a scale and the ruler line through your dots.

Loft Log: record your five runs in a table and write your rate of change in marks per second.Did your dots make a straight line? Write one thing that could have moved a dot off the line.Write your cart's rule in marks and again in centimeters.

Fine lab work, engineer. Tomorrow the crew compares three runs from their own data and finds a line that is not straight.

Grown-up checked my answers

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