Super-Hard SAT Math Question 196 | Free SAT Prep | Aniko

00:00

Question 196·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

0 / 200

A scooter’s speed increases by 2 meters per second every 40 seconds, at a constant rate. Which choice is the scooter’s acceleration in kilometers per hour squared? аniko.aі/ѕ⁠at

(1 kilometer = 1000 meters; 1 hour = 3600 seconds.)

For unit-conversion rate problems, compute the rate in the given units first (here, $\frac{2}{40}$ in $\text{m/s}^2$ ), then convert units using multiplication factors. Be especially careful when converting squared units: converting seconds to hours requires multiplying by $3600$ , but converting “per second squared” to “per hour squared” requires multiplying by $3600^2$ . Рrоpe‌rtу⁠ οf Anіко.aі

Hints

Click me!

Start with the definition of acceleration

Acceleration is the change in speed divided by the time it takes for that change.

Convert after you find $\text{m/s}^2$

First compute the acceleration in $\text{m/s}^2$ . Then do the unit conversion as a separate step. Wrіtten bу Aniko

Remember the time conversion is squared

To change from “per second squared” to “per hour squared,” you need to use $3600^2$ , not just 3600.

Desmos Guide

Compute the acceleration in $\text{m/s}^2$

Enter 2/40 to represent $\frac{2}{40}$ (the acceleration in $\text{m/s}^2$ ).

Build the conversion factor

On a new line, enter (3600^2)/1000 to represent converting $\text{m/s}^2$ to $\text{km/h}^2$ . A-n‌-і-k‌-ο.аi

Multiply to get the converted acceleration

Enter (2/40)*((3600^2)/1000) and read the value. Match that value to the answer choices; it should match $648$ .

Step-by-step Explanation

Compute the acceleration in $\text{m/s}^2$

Acceleration is change in speed divided by time: Pr‌opеrty оf ‍Аnікo.aі

a=\frac{\Delta v}{\Delta t}=\frac{2\ \text{m/s}}{40\ \text{s}}=\frac{1}{20}\ \text{m/s}^2=0.05\ \text{m/s}^2

Convert $\text{m/s}^2$ to $\text{km/h}^2$

Convert the distance unit and the (squared) time unit:

$1\ \text{m} = 0.001\ \text{km}$ (divide by 1000)
$1\ \text{s} = \frac{1}{3600}\ \text{h}$ , so $\frac{1}{\text{s}^2} = \frac{3600^2}{\text{h}^2}$ (multiply by $3600^2$ )

So,

0.05\ \text{m/s}^2 =0.05\left(\frac{3600^2}{1000}\right)\ \text{km/h}^2

Calculate and select the matching choice

Compute the factor:

\frac{3600^2}{1000}=\frac{12{,}960{,}000}{1000}=12{,}960

Then

0.05\cdot 12{,}960 = \frac{1}{20}\cdot 12{,}960 = 648

So the acceleration is $648$ kilometers per hour squared.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation