A rate of change compares the change in speed with the time it took. First find the speed gained per second, then convert meters to yards. Speed already has seconds in its denominator, and the rate adds another second, so both time units must become minutes. Converting only one gives a rate in the wrong units.
Hints
- Hint 1
A rate of change puts the change in speed over the time it took. Subtract the starting speed from the ending speed, then divide by the elapsed time. What units does that give you?
- Hint 2
A conversion factor is a fraction of equal measurements, so multiplying by it changes the units without changing the amount. Use feet as a bridge from meters to yards.
- Hint 3
The display measures speed in yards per minute, and the question asks how much that speed rises per minute. How many seconds in the rate’s denominator must become minutes?
Step-by-step
Find the rate, then convert its units
Step 1Write the rate of increase
The robot’s speed goes from to meters per second in seconds. The rate of change is speed gained divided by time elapsed, so
The units are meters per second per second, not meters per second.
- Step 2
Calculate the starting rate
Type in Desmos. It shows , so the robot gains meters per second of speed each second.
- Step 3
Change meters to yards
Each meter is feet, and each yard is feet, so multiply by to change meters to yards. Type in Desmos. It shows yards per second per second; the time units haven’t changed yet.
- Step 4
Convert both seconds to minutes
One minute factor converts the seconds inside speed; the other converts the seconds of elapsed time. Since minute is seconds, use the factor twice:
- Step 5
Read the display’s rate
Type in Desmos. It prints . So the displayed speed increases by yards per minute each minute. Choice A.