ENGR 215 ~ Dynamics Sections 12.1 – 12.2

Tutoring is a must!

• Monday and Wednesdays from 3-5 PM in

16-105.

• Dynamics is significantly harder than Statics.

IM

maF

The rules have

changed.

Rectilinear Kinematics: continuous motion along a line

dvvdsa

dt

sd

dt

dva

dt

dsv

2

2

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.

Constant Acceleration

)(2

2

1

022

002

0

ssavv

stvtas

tavv

co

c

c

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)

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

The modern solution….

integral (1/(0.02*s^2+12*s)^0.5) ds from 0 to 2000

Lecture Example 2: Graphical Solution