Question 52·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis
A drone's acceleration is 2.5 meters per second squared. Which choice gives this acceleration in kilometers per hour squared?
(1 kilometer = 1000 meters and 1 hour = 3600 seconds)
For unit-conversion rate problems, write the quantity with units and multiply by conversion fractions that cancel unwanted units. The key SAT trap here is the squared time unit: converting seconds to hours in requires squaring the conversion factor, so the number changes by a factor of , not .
Hints
Convert one unit at a time
First change meters to kilometers, then handle the seconds-to-hours part separately.
Watch the squared unit
Because the unit is “per second squared,” the seconds-to-hours conversion factor must be applied twice (squared).
Decide whether to multiply or divide
Ask: will the number get bigger or smaller when you switch from “per second squared” to “per hour squared”?
Desmos Guide
Enter the conversion expression
In Desmos, type:
2.5/1000*3600^2
This represents converting meters to kilometers (divide by 1000) and converting to (multiply by ).
Compare the result to the options
Read the computed value Desmos displays and choose the answer option that exactly matches it.
Step-by-step Explanation
Set up the unit conversions
Start with .
Convert meters to kilometers:
Convert seconds squared to hours squared:
Because the unit is , the factor must be squared.
Apply the distance conversion
Convert meters to kilometers:
Apply the time-squared conversion
Since , replacing seconds with hours in the denominator squared multiplies by :
So multiply the number by .
Compute and match to a choice
The correct choice is 32,400.