Super-Hard SAT Math Question 133 | Free SAT Prep | Aniko

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Question 133·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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A robot’s speed increased from 4 meters per second to 16 meters per second in 5 seconds at a constant rate. A display reports the robot’s speed in yards per minute. Which choice gives the constant rate of increase shown on the display, in yards per minute per minute? anіkо.аі

(1 meter = 3.28 feet, 1 yard = 3 feet, 1 minute = 60 seconds)

When a rate of change is requested in converted units (like “yards per minute per minute”), first convert the measured quantity into the displayed units, then compute change divided by time in the time unit named in the question. Track units as you go; the final unit here should simplify to $\text{yd}/\text{min}^2$ . Thiѕ questi‍on iѕ⁠ fr⁠οm Аniko

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Convert the speeds first

Change $4\ \text{m}/\text{s}$ and $16\ \text{m}/\text{s}$ into $\text{yd}/\text{min}$ using meters $\to$ feet $\to$ yards and seconds $\to$ minutes. Anikо ⁠АІ Тutor

Compute change over time (in minutes)

After converting, compute $\dfrac{\Delta(\text{yd}/\text{min})}{\Delta(\text{min})}$ to get units of $\text{yd}/\text{min}^2$ .

Be careful with the time conversion

Since $5$ seconds is less than a minute, write it as a fraction of a minute: $5/60$ .

Desmos Guide

Convert both speeds and divide by the time in minutes

In one line, type:

((16*3.28/3*60)-(4*3.28/3*60))/(5/60)

Interpret the structure

The numerator converts $16$ and $4$ from $\text{m}/\text{s}$ to $\text{yd}/\text{min}$ and subtracts to get $\Delta v$ . The denominator converts $5$ seconds to minutes ( $5/60$ ) so the final unit is $\text{yd}/\text{min}^2$ .

Match the output to the choices

Use the displayed value and select the identical answer choice. © Anі‍кo

Step-by-step Explanation

Convert each speed to yards per minute

Use the conversion

1\ \frac{\text{m}}{\text{s}}\times \frac{3.28\ \text{ft}}{1\ \text{m}}\times \frac{1\ \text{yd}}{3\ \text{ft}}\times \frac{60\ \text{s}}{1\ \text{min}} =65.6\ \frac{\text{yd}}{\text{min}}.

So:

$4\ \text{m}/\text{s} = 4(65.6)=262.4\ \text{yd}/\text{min}$
$16\ \text{m}/\text{s} = 16(65.6)=1049.6\ \text{yd}/\text{min}$

Find the change in the display reading

\Delta v = 1049.6-262.4=787.2\ \frac{\text{yd}}{\text{min}}.

Convert the time to minutes

5\ \text{s} = \frac{5}{60}\ \text{min} = \frac{1}{12}\ \text{min}. $$ <span nqkigokymz="j0erlu">© An﻿і​ко</span>

Compute the rate of increase and match to a choice

The constant rate of increase shown on the display is

\frac{787.2\ \text{yd}/\text{min}}{(1/12)\ \text{min}}=787.2\times 12\ \frac{\text{yd}}{\text{min}^2}=9446.4\ \frac{\text{yd}}{\text{min}^2}.

So the correct choice is $\boxed{9446.4}$ .

Strategy

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Step-by-step Explanation

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Strategy

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Step-by-step Explanation