Question 2

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The question

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A particle moves along the $x$ -axis. For $t \ge 0$ its velocity is

v(t) = \ln\!\left(t^2 - 4t + 5\right) - 0.2t.

$\text{(a)}$
There is exactly one time $t = t_R$ in $0 < t < 2$ when the particle is at rest. Find $t_R$ . For $0 < t < t_R$ , is the particle moving left or right? Give a reason.
$\text{(b)}$
Find the acceleration at $t = 1.5$ , showing the setup. Is the speed increasing or decreasing at $t = 1.5$ ? Explain.
$\text{(c)}$
The position at time $t$ is $x(t)$ , and $x(1) = -3$ . Find the position at $t = 4$ , showing the setup.
$\text{(d)}$
Find the total distance travelled over $1 \le t \le 4$ , showing the setup.

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Understanding the Question

This question is about a particle moving along the x-axis

Part 1 of 5

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The question

Calculator allowed

A particle moves along the $x$ -axis. For $t \ge 0$ its velocity is

v(t) = \ln\!\left(t^2 - 4t + 5\right) - 0.2t.

$\text{(a)}$
There is exactly one time $t = t_R$ in $0 < t < 2$ when the particle is at rest. Find $t_R$ . For $0 < t < t_R$ , is the particle moving left or right? Give a reason.
$\text{(b)}$
Find the acceleration at $t = 1.5$ , showing the setup. Is the speed increasing or decreasing at $t = 1.5$ ? Explain.
$\text{(c)}$
The position at time $t$ is $x(t)$ , and $x(1) = -3$ . Find the position at $t = 4$ , showing the setup.
$\text{(d)}$
Find the total distance travelled over $1 \le t \le 4$ , showing the setup.

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This question is about a particle moving along the x-axis

Part 1 of 5