A speed increase over a stated time signals acceleration: speed change divided by elapsed time. Speed already has time in its denominator, so acceleration has time squared there. Convert distance once and convert the time unit twice; then enter the complete numeric chain in Desmos. Converting time only once leaves the wrong units, even if the arithmetic looks convincing.
Hints
- Hint 1
An acceleration tells you how quickly speed changes. Divide the speed gain by the time it takes. Since speed already means distance per second, what time unit will be left underneath?
- Hint 2
A conversion factor is a fraction made from two equal amounts. Put meters on the bottom of the kilometer-to-meter factor so they cancel the meters in the acceleration.
- Hint 3
Meters per second squared has two seconds in the denominator. Use the seconds-per-hour factor twice, or square the whole factor. Desmos can evaluate the numbers, but it won't check the units for you.
Step-by-step
Build the acceleration unit by unit
Step 1Find the rate of speed change
Acceleration means speed change divided by elapsed time. The scooter gains meters per second of speed in seconds, so
The seconds are squared because one comes from the speed unit and another comes from the elapsed time.
- Step 2
Change meters to kilometers
A conversion factor equals because its top and bottom describe the same distance. Put meters underneath so meters cancel:
The unit left on top is kilometers.
- Step 3
Convert both seconds
Seconds appear twice underneath. Put seconds on top of the seconds-per-hour factor, then square the entire time conversion factor to cancel both copies:
Only kilometers per hour squared remain. Using the time factor once would leave one second in the unit.
- Step 4
Evaluate the conversion
Type into Desmos. It displays , so the scooter's acceleration is kilometers per hour squared. Choice B.