Physics 218 Mechanics Instructor Dr Tatiana Erukhimova Lecture
- Slides: 15
Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 3
If a=ac=Const:
Problems 1. An experimental vehicle starts from rest at t=0 and accelerates at a rate given by a = 5 m/s 3 t. What is its velocity and position 2 s later? 2. A particle moves along the x axis. Its position as a function of time is given by x(t) = at+bt 2 where t is in sec and x is in meters. a and b are constants. What is the acceleration as a function of time? 3. a(t) = α t 2. v(t = 0) = W; x(T) = D. α, T, W, and D are constants. Find the velocity and position as a function of time.
A “police car” problem x 2 – x 1 = 3. 5 km x=0 x 1 V 1=30 m/s a=const V(t=0)=0 x 2 V 2=40 m/s V 3=20 m/s a=0 ap=kt You start moving from rest with constant acceleration. There is a police car hiding behind the tree. The policeman has a metric radar. He measures your velocity to be 30 m/s. While the policeman is converting m/s to mph, you continue accelerating. You meet another police car. This policeman measures your velocity to be 40 m/s. You also notice the police, drop your velocity to 20 m/s and start moving with a constant velocity. However, it is too late. This police car starts chasing you with acceleration kt (k is a constant). After some distance he catches you.
A “police car” problem x 2 – x 1 = 3. 5 km x=0 x 1 V 1=30 m/s a=const V(t=0)=0 x 2 V 2=40 m/s V 3=20 m/s a=0 ap=kt 1. What was your acceleration before you meet the second police car? 2. How long did you travel from x 1 to x 2? 3. Find x 1 4. At which distance does the police car catch you? 5. Convert the velocity from m/s to mph
Free fall On planet Earth, if you neglect air resistance, any body which is dropped will experience a constant acceleration, called g, independent of its size or weight. g=9. 8 m/s 2=32 ft/s 2 g-positive!
Galileo Galilei (1564 -1624), the basic law of motion a a = g = const v for all bodies independently on their masses
Galileo's “Law of Falling Bodies” distance (S) is proportional to time (T) squared
Galileo’s notes
Free fall
A ball is dropped vertically down (no air resistance) from height H. Find the position x(t) and velocity v(t) of the ball as a function of time. How long is the ball in the air?
A person throws a ball upward into the air with an initial velocity of 15 m/s. Calculate a) How much time does it take for the ball to reach the maximum height? b) How high does it go? c) How long is the ball in the air before it comes back to the thrower’s hands d) The velocity of the ball when it returns to the thrower’s hand e) At what time t the ball passes a point 8. 00 m above the person’s hand
Have a great day! Chapters 3, 4 videos Reading: Chapters 3, 4 Chapters 2, 3 problems and exercises
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