Name: ______
AP Calculus AB --Notes
What is rectilinear motion?
Rectilinear motion means motion along a straight line. This is a useful topic to study for learning how to describe the movement of cars along a straight road or of trains along straight railway tracks. In this section you have only two directions to worry about: (1) along the direction of motion, and (2) opposite to the direction of motion.
To illustrate this imagine a train heading east.
If it is accelerating away from the station platform (P), the direction of acceleration is the same as the direction of the train's velocity — east. If it is braking the direction of acceleration is opposite to the direction of its motion, i.e. west.
**Imagine a ball thrown up in the air. Graph:
Acceleration due to gravity is ALWAYS ______. On the way up, the velocity of the ball is ______(slope of tangent would be +). Is the ball speeding up or slowing down? ______On the way down, the ball’s velocity is ______. Is the ball speeding up or slowing down?______
**If acceleration and velocity have the SAME SIGNS, then the object is ______.
If acceleration and velocity have DIFFERENT SIGNS, then the object is ______.
t - time
s(t) – position Average Velocity =
v(t) – velocity
a(t) – acceleration Instantaneous Velocity = derivative
Example 1:
A particle’s position is given by the equation .
a) What is the particle’s velocity at time t?
b) What is the particle’s velocity when t = 3? When t = 5?
c) When is the particle at rest?
d) When is the particle moving forward?
e) When is the particle moving backwards?
f) Draw a diagram illustrating the motion of this particle
g) Find the total distance traveled by the particle during the first 6 seconds of its motion.
h) What is the particle’s acceleration at time t?
Review Example:
If a man tosses a baseball vertically upward at a rate of 64 ft/sec.
a) When does the baseball return to his hands?
b) What is the velocity of the ball when it returns to his hands?
c) What is the average velocity during the first 2 seconds?
d) What is the acceleration of the baseball after 2 seconds?