A motor powers a model car so that after starting from rest, the car travels s inches in t seconds,where s=16t\sqrtt. Which of the following gives the average speed of the car, in inches per second, over the first t seconds after it starts?

SAT Mathematics Practice Test 6

Question : 49 of 58

Marks: +1, -0

A motor powers a model car so that after starting from rest, the car travels s inches in

t

seconds,where

s=16t√t

. Which of the following gives the average speed of the car, in inches per second, over the first t seconds after it starts?

$4√t$
$16√t$
$16/√t$
$16t$

Validate

Solution:

The average speed of the model car is found by dividing the total distance traveled by the car by the total time the car traveled. In the first t seconds after the car starts,the time changes from 0 to t seconds. So the total distance the car traveled is the distance it traveled at t seconds minus the distance it traveled at 0 seconds. At 0 seconds, the car has traveled

16(0)√0

inches, which is equal to 0 inches. According to the equation given, after

t

seconds, the car has traveled

16t√t

inches. In other words, after the car starts, it travels a total of

16t√t

inches in t seconds. Dividing this total distance traveled by the total time shows the car’s average speed:

{16t√t}/t=16√t

inches per second.
Choices A, C, and D are incorrect and may result from misconceptions about how average speed is calculated.

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