Question

A particle moves according to a law of motion s = f(t), t ≥ 0, where...

A particle moves according to a law of motion

s = f(t), t ≥ 0,

where t is measured in seconds and s in feet.

f(t) = t3 − 15t2 + 72t

(a) Find the velocity at time t.
v(t) =

(b) What is the velocity after 5 s?

v(5) =

(c) When is the particle at rest?

t =   s (smaller value)
t =   s (larger value)

When is the particle moving in the positive direction? (Enter your answer in interval notation.)

t

Find the total distance traveled during the first 7 s.
ft

When, for

0 ≤ t < ∞,

is the particle speeding up? (Enter your answer in interval notation.)

When, for

0 ≤ t < ∞,

is it slowing down? (Enter your answer in interval notation.)

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t3 − 15t2 + 72t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = (c) When is the particle at rest? t =   s (smaller value) t =   s (larger value) When is the particle moving in the positive direction? (Enter your answer in interval...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 23t (a) Find the velocity at time t. v(t) =    ft/s (b) What is the velocity after 1 second? v(1) =   ft/s (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t (a) Find the velocity at time t. v(t) = ft/s (b) What is the velocity after 1 second? v(1) = ft/s (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 26t A. Find the acceleration at time t and after 1 second. a(t) = ft/s2 a(1) = ft/s2 B. When is the particle speeding up? (Enter your answer using interval notation.) c. When is it slowing down? (Enter your answer using...
A particle moves according to a law of motion , , where is measured in seconds...
A particle moves according to a law of motion , , where is measured in seconds and in feet. Find the velocity at time . What is the velocity after second? When is the particle at rest? When is the particle moving in the positive direction? Find the total distance traveled during the first seconds. Draw a diagram like Figure 2 to illustrate the motion of the particle. Find the acceleration at time and after second. Graph Icon Graph the...
The function s(t) describes the position of a particle moving along a coordinate line, where s...
The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t) = 3t2 - 6t +3 A) Find the anti-derivative of the velocity function and acceleration function in order to determine the position function. To find the constant after integration use the fact that s(0)=1. B) Find when the particle is speeding up and slowing down. C) Find the total distance from time 0 to time...
A particle moves along a line with velocity v(t)=(3 - t)(2+t), find the distance traveled during...
A particle moves along a line with velocity v(t)=(3 - t)(2+t), find the distance traveled during the time interval [0, 1].
A particle moves in a straight line with velocity 8-2t ft/s. Find the total displacement and...
A particle moves in a straight line with velocity 8-2t ft/s. Find the total displacement and total distance traveled over the time interval [0, 7].
A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and moves...
A particle starts from the origin with velocity 5 ?̂m/s at t = 0 and moves in the xy plane with a varying acceleration given by ?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and t is in seconds. i) Determine the VELOCITY and the POSITION of the particle as a function of time.
A particle moves in a straight line and its position is given by s(t)=t^3 - 6t^2-36t...
A particle moves in a straight line and its position is given by s(t)=t^3 - 6t^2-36t +66, where s is measured in feet and t in seconds. Find the intervals when the particle increases its speed.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT