(h) When, for 0 st < ∞, is the particle speeding up? (Enter your answer in interval notation.)
(h) When, for 0 st < ∞, is the particle speeding up? (Enter your answer in interval notation.)
Related questions
Question
How do you solve D, E, and H?
Transcribed Image Text:(h) 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.)
Transcribed Image Text: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) = t - 9t + 15t
(a) Find the velocity at time t.
v(t) = 31 – 18t + 15
(b) What is the velocity after 4 s?
v(4) = |-9
ft/s
(c) When is the particle at rest?
|s (smaller value)
|s (larger value)
t = 1
t = 5
(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.)
te
(e) Find the total distance traveled during the first 8 s.
ft
(f) Find the acceleration at time t.
a(t) =
6t – 18
Find the acceleration after 4 s.
a(4) =
6
ft/s²
(g) Graph the position, velocity, and acceleration functions for the first 8 s.
y
y
40
40
30
30
20
20
10
10
4
8
4
8
-10F a
- 10 a
- 20
- 20
-30야
-30
y
y
40야
40
30
30
20아
20
10
10
t
4
6
8
4
8
- 10 s
- 10 v
- 20
- 20
-30
- 30
Expert Solution
Step 1
(D)
Given:
The displacement of the particle as a function of time is .
Introduction:
Displacement is defined as the change in the position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
