Suppose that the position of a particle is given by s(t)=3t^3+6t+9 (a) Find the velocity at time t. v(t)= ? (b) Find the velocity at time t=3 seconds. ? Find the acceleration at time tt. a(t) = ? m/s^2 (d) Find the acceleration at time t=3 seconds.

Suppose that the position of a particle is given by s(t)=3t^3+6t+9 (a) Find the velocity at time t. v(t)= ? (b) Find the velocity at time t=3 seconds. ? Find the acceleration at time tt. a(t) = ? m/s^2 (d) Find the acceleration at time t=3 seconds.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Question

Suppose that the position of a particle is given by s(t)=3t^3+6t+9

(a) Find the velocity at time t.

v(t)= ?

(b) Find the velocity at time t=3 seconds.
?

Find the acceleration at time tt.

a(t) = ? m/s^2

(d) Find the acceleration at time t=3 seconds.

Expert Solution

Step 1

Given that, $s = 3 t^{3} + 6 t + 9$

Now, we have,

$v (t) = \frac{d}{d t} (s (t)) = \frac{d}{d t} (3 t^{3} + 6 t + 9) = 3 \frac{d}{d t} (t^{3}) + 6 \frac{d}{d t} (t) + \frac{d}{d t} (9) = 9 t^{2} + 6$

So, velocity at t=3 seconds will be,

$v (3) = 9 {(3)}^{2} + 6 = 9 \times 9 + 6 = 81 + 6 = 87 u n i t$

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