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Tutoring is a must!
• Monday and Wednesdays from 3-5 PM in
16-105.
• Dynamics is significantly harder than Statics.
Constant Acceleration
• If acceleration is constant, determine the velocity and position as a function of time.– assume an initial velocity of vo, and an initial position
of so.
• Determine the velocity as a function of position.
Lecture Example 1: Position of a particle on a straight line
s(t) = 1.5 t3 – 13.5t2 + 22t
• Determine the position of the particle at t = 6 s.• Determine the total distance traveled in 6 seconds.• Determine the acceleration of the particle at t = 6s.
Particle moving on a straight line
-60
-40
-20
0
20
40
60
0 1 2 3 4 5 6 7
Time (sec)
Position (m)
Velocity (m/s)
Particle moving on a straight line
-60
-40
-20
0
20
40
60
0 1 2 3 4 5 6 7
Time (sec)
Positon (m)
Velocity (m/s)
Acceleration (m/s2)
Lecture Example 2:
The acceleration of a rocket traveling upward is given by a = (6+0.02s) m/s2. Determine the rocket’s velocity when s=2 km, and the time needed to reach that this altitude. Initially v=0, s=0, and t=0.
Intergration of Hard Problems
• Schaum’s Mathematical Handbook 14.280
• Numerical Integration using Ti-84 or Ti-89– Ti-84 fnInt(1/(ax^2+bx+c)^0.5,x,llim,ulim)– Ti-89 (1/(ax^2+bx+c)^0.5,x,llim,ulim)
)22ln(1 2
2baxcbxaxa
acbxax
dx
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