particle moves according to a law of motion -ro, t20. where t measured in seconds and s in feet. (If an answer does not kist, enter DNE.) f(t) = t3 - 8t2 + 24t (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?
particle moves according to a law of motion -ro, t20. where t measured in seconds and s in feet. (If an answer does not kist, enter DNE.) f(t) = t3 - 8t2 + 24t (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?
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Transcribed Image Text:particle moves according to a law of motion .. 10). t20. where t
measured in seconds and s in feet. (If an answer does not
kist, enter DNE.)
s = f(t),
f(t) = t3 – 8t2 + 24t
(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 answer using interval notation.)
(e) Find the total distance traveled during the first 6
seconds.
ft
(f) Draw a diagram like this figure to illustrate the motion
of the particle.
S
t = 0
S= 0
t = 6
s= 72
t = 0
s = 0
t = 6
s= 72
t = 0
8
t =
t = 0
t =
3
1600
S= 0
S= 0
1600
S =
27
27
(g) Find the acceleration at time t and after 1 second.
a(t) =
ft/s2
a(1) =
ft/s²
(h) Graph the position, velocity, and acceleration functions
for 0sts6. (A graphing calculator is recommended.)
60
60
40
40
20
20
3
4
5
4
- 20
- 20
60
60
40
40
20
20
3
6.
3
5
a
- 20
- 20
(i) When is the particle speeding up? (Enter your answer
using interval notation.)
When is it slowing down? (Enter your answer using interval
notation.)
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