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Herman is riding his hoverboard. The function
V gives Herman's velocity (in meters per second),
t seconds after he started riding.
What is the best interpretation for the following statement?
The value of the derivative of
V at
t=5 is equal to 1.5 .
Choose 1 answer:
A) During the first 5 seconds, Herman's acceleration is 1.5 meters per second squared.
(B) After 5 seconds, Herman's acceleration is 1.5 meters per second squared.
(C) After 5 seconds, Herman's velocity is 1.5 meters per second.
(D) After 5 seconds, Herman's acceleration is 1.5 .

Herman is riding his hoverboard. The function $V$ gives Herman's velocity (in meters per second), $t$ seconds after he started riding. $\newline$ What is the best interpretation for the following statement? $\newline$ The value of the derivative of $V$ at $t=5$ is equal to $1$ . $5$ . $\newline$ Choose $1$ answer: $\newline$ A) During the first $5$ seconds, Herman's acceleration is $1$ . $5$ meters per second squared. $\newline$ (B) After $5$ seconds, Herman's acceleration is $1$ . $5$ meters per second squared. $\newline$ (C) After $5$ seconds, Herman's velocity is $1$ . $5$ meters per second. $\newline$ (D) After $5$ seconds, Herman's acceleration is $1$ . $5$ .

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. Herman is riding his hoverboard. The function

V

gives Herman's velocity (in meters per second),

t

seconds after he started riding.

\newline

What is the best interpretation for the following statement?

\newline

The value of the derivative of

V

at

t=5

is equal to

1

.

5

.

\newline

Choose

1

answer:

\newline

A) During the first

5

seconds, Herman's acceleration is

1

.

5

meters per second squared.

\newline

(B) After

5

seconds, Herman's acceleration is

1

.

5

meters per second squared.

\newline

(C) After

5

seconds, Herman's velocity is

1

.

5

meters per second.

\newline

(D) After

5

seconds, Herman's acceleration is

1

.

5

.

Acceleration Definition: The derivative of $V$ with respect to $t$ represents Herman's acceleration at a specific moment in time.
Derivative at $t=5$ : Since the derivative at $t=5$ is $1.5$ , this means that at $t=5$ seconds, Herman's instantaneous acceleration is $1.5$ meters per second squared.
Velocity vs Acceleration: This information does not tell us about Herman's velocity, only his acceleration at that specific time.
Correct Interpretation: Therefore, the correct interpretation of the statement is that after $5$ seconds, Herman's acceleration is $1.5$ meters per second squared.

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