Suppose that the height of a particle is given by s(t) = t³ - 17t + 41, t≥ 0, where t is measured in seconds and the height is measured in meters. (a) Find the velocity at time t. v(t) = V= (b) Find the velocity at time t = 3 seconds. (c) When is the particle at rest? t = m m S S seconds (d) When is the particle moving in a downward direction? 4
Suppose that the height of a particle is given by s(t) = t³ - 17t + 41, t≥ 0, where t is measured in seconds and the height is measured in meters. (a) Find the velocity at time t. v(t) = V= (b) Find the velocity at time t = 3 seconds. (c) When is the particle at rest? t = m m S S seconds (d) When is the particle moving in a downward direction? 4
Transcribed Image Text:Suppose that the height of a particle is given by \( s(t) = t^3 - 17t + 41, \, t \geq 0 \), where \( t \) is measured in seconds and the height is measured in meters.
(a) Find the velocity at time \( t \).
\[ v(t) = \underline{\phantom{m/s}} \ m/s \]
(b) Find the velocity at time \( t = 3 \) seconds.
\[ v = \underline{\phantom{m/s}} \ m/s \]
(c) When is the particle at rest?
\[ t = \underline{\phantom{\text{seconds}}} \ \text{seconds} \]
(d) When is the particle moving in a downward direction?
\[ \underline{\phantom{\text{seconds}}} \ \text{seconds} \]
(e) Find the total distance traveled by the particle during the first 7 seconds of travel.
(Round your answer to the nearest hundredths place.)
\[ \underline{\phantom{\text{meters}}} \ \text{meters} \]
(f) Find the acceleration at time \( t \).
\[ a(t) = \underline{\phantom{m/s^2}} \ \frac{m}{s^2} \]
(g) Find the acceleration at time \( t = 7 \) seconds.
\[ a = \underline{\phantom{m/s^2}} \ \frac{m}{s^2} \]
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Given query is to find the velocity function and velocity at different points.
![Suppose that the height of a particle is given by \( s(t) = t^3 - 17t + 41, \, t \geq 0 \), where \( t \) is measured in seconds and the height is measured in meters.
(a) Find the velocity at time \( t \).
\[ v(t) = \underline{\phantom{m/s}} \ m/s \]
(b) Find the velocity at time \( t = 3 \) seconds.
\[ v = \underline{\phantom{m/s}} \ m/s \]
(c) When is the particle at rest?
\[ t = \underline{\phantom{\text{seconds}}} \ \text{seconds} \]
(d) When is the particle moving in a downward direction?
\[ \underline{\phantom{\text{seconds}}} \ \text{seconds} \]
(e) Find the total distance traveled by the particle during the first 7 seconds of travel.
(Round your answer to the nearest hundredths place.)
\[ \underline{\phantom{\text{meters}}} \ \text{meters} \]
(f) Find the acceleration at time \( t \).
\[ a(t) = \underline{\phantom{m/s^2}} \ \frac{m}{s^2} \]
(g) Find the acceleration at time \( t = 7 \) seconds.
\[ a = \underline{\phantom{m/s^2}} \ \frac{m}{s^2} \]](https://content.bartleby.com/qna-images/question/03532cdf-3ae3-42ec-b6da-b6f111ab5ca1/b866a7fd-7f8f-4a18-867a-d18b588cf5ce/3jseuji_processed.jpeg)
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