2.7 EXERCISES1-4 A particle moves according to a law of motion s f(t),t 0, where t is measured in seconds ands in feet.(a) Find the velocity at time t.(b) What is the velocity after 1 second?(c) When is the particle at rest?(d) When is the particle moving in the positive direction?(e) Find the total distance traveled during the first 6 seconds.(f) Draw a diagram like Figure 2 to illustrate the motion of theparticle.(g) Find the acceleration at time t and after 1 second.(h) Graph the position, velocity, and acceleration functionsfor 0t 6.(i) When is the particle speeding up? When is it slowing down?1. f(t) t3-9t224t2. f(t) 0.01t - 0.04t3

Question
Asked Oct 17, 2019

2.7

Can you show me the steps to solve step e?

1) f(t) = t^3 - 9t^2 +24t

e) Find the total distance travelled during the first 6 seconds.

2.7 EXERCISES
1-4 A particle moves according to a law of motion s f(t),
t 0, where t is measured in seconds ands in feet.
(a) Find the velocity at time t.
(b) What is the velocity after 1 second?
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction?
(e) Find the total distance traveled during the first 6 seconds.
(f) Draw a diagram like Figure 2 to illustrate the motion of the
particle.
(g) Find the acceleration at time t and after 1 second.
(h) Graph the position, velocity, and acceleration functions
for 0t 6.
(i) When is the particle speeding up? When is it slowing down?
1. f(t) t3-9t224t
2. f(t) 0.01t - 0.04t3
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2.7 EXERCISES 1-4 A particle moves according to a law of motion s f(t), t 0, where t is measured in seconds ands in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance traveled during the first 6 seconds. (f) Draw a diagram like Figure 2 to illustrate the motion of the particle. (g) Find the acceleration at time t and after 1 second. (h) Graph the position, velocity, and acceleration functions for 0t 6. (i) When is the particle speeding up? When is it slowing down? 1. f(t) t3-9t224t 2. f(t) 0.01t - 0.04t3

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check_circleExpert Solution
Step 1
(e)
Consider the given model function for motion of a particle as f(t)=f -9t2 +24t
From part (a), the velocity of the particle at time t is given by;
d
(t-9r224t
dt
= 3t2-18t 24
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(e) Consider the given model function for motion of a particle as f(t)=f -9t2 +24t From part (a), the velocity of the particle at time t is given by; d (t-9r224t dt = 3t2-18t 24

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