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www-awualekscom/alelscgi/X/slexe/to_u-lgNsikasNW8D8A9PVVie Ic
Craphs and functions
Word problom involving composition of two functions
The braking distance
D(v) (in meters) for a certain car moving at velocity
v (in meters/second) is given by
D(v)=(v^(2))/(22)
The car's velocity
B(t) (in meters/second)
t seconds after starting is given by
B(t)=9t.
Write a formula for the braking distance
S(t) (in meters) after
t seconds.

www-awualekscom/alelscgi/X/slexe/to_u-lgNsikasNW $8$ D $8$ A $9$ PVVie Ic $\newline$ Craphs and functions $\newline$ Word problom involving composition of two functions $\newline$ The braking distance $D(v)$ (in meters) for a certain car moving at velocity $v$ (in meters/second) is given by $D(v)=\frac{v^{2}}{22}$ $\newline$ The car's velocity $B(t)$ (in meters/second) $t$ seconds after starting is given by $B(t)=9 t$ . $\newline$ Write a formula for the braking distance $S(t)$ (in meters) after $t$ seconds.

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. www-awualekscom/alelscgi/X/slexe/to_u-lgNsikasNW

8

D

8

A

9

PVVie Ic

\newline

Craphs and functions

\newline

Word problom involving composition of two functions

\newline

The braking distance

D(v)

(in meters) for a certain car moving at velocity

v

(in meters/second) is given by

D(v)=\frac{v^{2}}{22}

\newline

The car's velocity

B(t)

(in meters/second)

t

seconds after starting is given by

B(t)=9 t

.

\newline

Write a formula for the braking distance

S(t)

(in meters) after

t

seconds.

Identify Functions: Identify the functions given and the function to be found. $\newline$ We have $D(v) = \frac{v^2}{22}$ for braking distance based on velocity, and $B(t) = 9t$ for velocity based on time. We need to find $S(t)$ , the braking distance as a function of time.
Substitute and Find: Substitute the expression for $B(t)$ into $D(v)$ to find $S(t)$ . $\newline$ Since $D(v) = \frac{v^2}{22}$ and $B(t) = 9t$ , substituting $B(t)$ into $D(v)$ gives: $\newline$ $S(t) = \frac{(9t)^2}{22}$
Simplify Expression: Simplify the expression for $S(t)$ . $\newline$ $S(t) = \frac{81t^2}{22}$ $\newline$ This is the formula for the braking distance in meters after $t$ seconds.

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