Download 2 Sept 10 Acceleration

Acceleration
Exercise
The motion of a particle in the x-direction is given by:
x  4  27t  t
3
a) Find the velocity function, v(t)
b) Find the acceleration function, a(t)
c) When (if ever) is the velocity v=0? What is the acceleration
and position at that time?
Exercise
Draw x(t), v(t) and a(t) diagrams to describe the motion. Stack the
graphs vertically so that a vertical line connects equal values of t
on each of the three graphs.
V0>0
Constant acceleration
A useful special case of motion is that of constant acceleration,
where a(t)=aavg=a for all times t.
a) Write an equation to
describe the velocity v(t)
at any time t. What does
this look like graphically?
b) Write an equation to
describe the position x(t)
at any time t. What does
this look like graphically?
Constant acceleration
Objects in gravitational free-fall experience constant acceleration.
The acceleration depends on the location on Earth, and height
above the surface, but we will approximate:
g  9.8m / s
2
This is independent
of the mass of the
falling body! We
will revisit this
amazing fact later.
Sample Problems
Sample 2-7: A pitcher tosses a baseball up along a y axis, with an
initial speed of 12 m/s.
a) How long does the ball take to
reach its maximum height?
b) What is the ball’s maximum
height above its release point?
c) How long does the ball take to
reach a point 5.0 m above its
release point?
Applets
http://wps.aw.com/aw_young_physics_11
1.1 Analyzing Motion Using Diagrams
1.2 Analyzing Motion Using Graphs
1.3 Predicting Motion from Graphs
1.4 Predicting Motion from Equations
1.7 Problem