WHAT IS NASA PHYSICS?
MODULES
Forces and Motion
Conservation of Momentum & Energy
Temperature and Heat
Fluids
Optics
Electromagnetic Spectrum
Modern Physics
Anticipation Guide 7
Intro to Modern Physics
Blackbody Radiation
The Ultraviolet Catastrophe
The Photoelectric Effect
Bohr's Atom
Spectra
Radioactive Decay
Special Relativity (SR)
Simultaneity
Distance and Time
General Relativity
May the Forces be with You
Modern Physics Notebook
Assessment Problems 7
Useful Things
SITE MAP
Forces and Motion
Anticipation Guide
Speed and Velocity
Acceleration
Gravity
Projectile Motion
Orbital Motion
Newton's Laws of Motion
Assessment Problems
Equation
velocity =
acceleration x time
v = at
1.4
Equation
final velocity = initial velocity + acceleration x time
v_{f} = v_{i }+ at
1.5
Equation
average velocity = initial velocity + final velocity ÷ two
v_{ave} = (v_{i} + v_{f}) / 2
1.6
Equation
distance traveled = ½ x acceleration x times squared
d = ½ at^{2}
1.7
Acceleration
Example Question
If a plane on an aircraft carrier accelerates from rest to 90 m/s in 3 seconds, its average acceleration from Eqn 1.3 is:
a = v/t = (90 m/s)/3 s = 30 m/s^{2}
The speed or velocity that the plane is moving can also be calculated knowing its acceleration and the amount of time it has been accelerating. Just rearrange equation (1.3) to get:
velocity = acceleration x time v = at
If an object was already moving and then accelerated, its final velocity, vf, is:
Or more generally, final velocity = initial velocity + acceleration x time v_{f} = v_{i} + at
In many problems, such as this one, the initial velocity, v_{i}, is zero.
Of course, the plane needs to accelerate to 90 m/s this speed (if that is what it takes to become airborne) before it goes careening off the bow of the aircraft carrier into the ocean. So, you might ask, how far has the plane traveled in the 3 seconds it took for it to accelerate to 90 m/s? We can figure this out by mathematically juggling things you already know.
Since from Eqn 1.1: v = d/t, then d = vt or distance equals velocity x time, which is true for the average velocity. By definition the average velocity is found by adding initial and final velocities and dividing by 2 (or multiplying by ½):
v_{ave} = ½ (v_{i} + v_{f})
d = ½ (v_{i} + v_{f}) t
Now we substitute what v_{f} is from equation 1.5 into this to solve for distance traveled in terms of time and acceleration:
d = ½ (v_{i} + v_{i} + at) t
now add the two vi together:
d = ½ (2vi + at) t
now multiply each term by t:
d = ½(2v_{i} t+ at^{2})
finally, divide each term by 2:
d = v_{i} t+ ½at^{2}
and if v_{i} is zero, then
distance traveled = ½ x acceleration x times squared d = ½ at^{2}
So, how far did the plane travel in 3 seconds?
d = ½ at^{2} = ½ x 30 x 3^{2} = 15 m/s^{2} x 9 s^{2} = 135 m
And how long are aircraft carriers? The largest, such as the USS Nimitz, is 333 m long, providing plenty of room to accelerate fast enough for a safe takeoff!
When you first glanced at this page and saw the equations you may have groaned that physics is difficult. But I hope that as you read through the equations you saw that each step is easy and logical. If so you are beginning to think like a physicist!
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