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A particle moves along the
x-axis so that at time
t >= 0 its velocity is given by
v(t)=-2t+3. Determine the acceleration of the particle at
t=9.
Answer:

A particle moves along the $x$ -axis so that at time $t \geq 0$ its velocity is given by $v(t)=-2 t+3$ . Determine the acceleration of the particle at $t=9$ . $\newline$ Answer:

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. A particle moves along the

x

-axis so that at time

t \geq 0

its velocity is given by

v(t)=-2 t+3

. Determine the acceleration of the particle at

t=9

.

\newline

Answer:

Identify Relationship: Identify the relationship between velocity and acceleration. $\newline$ Acceleration is the derivative of velocity with respect to time. To find the acceleration at any time $t$ , we need to differentiate the velocity function $v(t)$ with respect to $t$ .
Differentiate Velocity Function: Differentiate the velocity function $v(t) = -2t + 3$ . $\newline$ The derivative of $-2t$ with respect to $t$ is $-2$ , and the derivative of a constant $3$ is $0$ . Therefore, the acceleration function $a(t)$ is the constant $-2$ .
Evaluate Acceleration at $t=9$ : Evaluate the acceleration function at $t=9$ . Since the acceleration function $a(t)$ is a constant $-2$ , the acceleration at any time $t$ , including $t=9$ , is $-2$ .

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? You may use a calculator and round your answer to the nearest thousandth.

\newline

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