x(t) for constant acceleration

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x(t) for constant acceleration
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v(t) for constant acceleration
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Average velocity
therefore
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4 equations to use for constant acceleration
phenomena (only)
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4 equations to use for constant acceleration
phenomena (only)
Variables x x0 v v0 a t
If you know 4 (or sometimes 3) variables, you can
solve for the other variables.
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Constant Acceleration (Problem Solving)

1. Identify the main idea of the problem if it is
   readily apparent. For example, constant
   acceleration.
2. Draw pictures, label objects, write knowns and
   unknowns. Use subscripts with variables if there
   are multiple objects in the problem.
3. Write physics equations, definitions, and laws
   that might help solve the problem.
4. Do the math.
5. Check your work. Does the answer make sense?

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Example
A softball player is running at full speed toward
second base with a speed of 12 m/s. She slides
for 1.5 m into second base. Assuming constant
acceleration, (1) how much time elapses as she is
sliding and (2) What is her acceleration?
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Example
Motorcycles have amazing acceleration. The
Kawasaki Ninja ZX-14 can reportedly accelerate
from 0 to 60 mph in 2.5 s. What is its
acceleration and how far does it travel during
this time interval?
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Free-fall
An free object rising or falling near Earth,
with negligible air resistance, is a special case
of motion with constant acceleration.
y (m)
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Equations of motion for free-fall
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Example
A diver steps off a 10-m platform. If she starts
from rest (approximately) at t0, how fast is she
moving and what is the clock reading when she
hits the water?
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Example
A tennis player is working on his serve. He wants
to toss the tennis ball vertically exactly 1.5 m
above where the ball leaves his hand. With what
speed must the ball leave his hand?
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Example
A batter hits a pop-fly that travels straight
upward and is ultimately caught by the catcher.
(a) If the speed of the ball after colliding with
the bat is 30 m/s, what maximum height (above the
bat) will the ball travel? (b) What is the
velocity of the ball when it is caught by the
catcher?