2. The position function of a moving object is s(t)= t³(3-t), 120 in metres, at time t, in seconds. a. Calculate the object's velocity and acceleration at any time t. b. After how many seconds does the object stop? c. When does the motion of the object change direction? d. When does the object return to its original position?
2. The position function of a moving object is s(t)= t³(3-t), 120 in metres, at time t, in seconds. a. Calculate the object's velocity and acceleration at any time t. b. After how many seconds does the object stop? c. When does the motion of the object change direction? d. When does the object return to its original position?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me is this correct for the question. And please complete part d) show all your work
Transcribed Image Text:2. The position function of a moving object is s(t)= t³(3-t), r=0 in metres, at time 7, in seconds.
a. Calculate the object's velocity and acceleration at any time .
b. After how many seconds does the object stop?
c. When does the motion of the object change direction?
d. When does the object return to its original position?
૫૦૦ ૩૧/૧૦/H
Transcribed Image Text:#2 s(t)=+³ (3-4), (20
a) Velocity
V=
ds
dt = +²³(-1) = 5t4 (3-6)
Acceleration
4
-6t³ + 15t" m/s
ds
A = d² ² = a (-66² + 15 (4)
Hence,
d
= (-61³) + (1514)
3
= - 30t4 + 60€ ³ m/s
b) Let I be the time when the object stop, so v=0 when t = I
0 = -6+³ + 1ST" (using part (a))
=) T² (-6T +15) = (
=) -6 + 15 = 0 (;. T # ()
15. 5
T²
=> √ = = 16² = ²2²2²2² = 4.5
The required time is 4.5 sec for the object to stop
The motion of the object changes its direction when the
acceleration becomes 0.
dsz
Let I' be the time when the object changes its directich so,
बदर
3
0$ = = 0 => -30T¹² +
60T1³ = 0 (use part (a))
= 0 => -30T₁²4 + 6071³ = 0 (0₂
¹1=T'
=> T'3 (-30T' +60) = (
=2-307/ + 60 = 0 (²₁ T² # 0)
=> T² =2
The required time is 2 for the motion of the object to change
direction
Hebre
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