acceleration: definitions and units.
Constant acceleration is when a bodys velocity changes uniformly wrt time. The most common experience of such acceleration is to watch something falling, it is constantly accelerated due to gravity, the force of attraction between 2 masses.
There are 3 equations of motion that factor in constant acceleration
Acceleration is described as the rate of change of velocity with respect to time.
Lets check it out at http://www.walter-fendt.de/ph14e/acceleration.htm
Here we can check out some graphs comparing x/t, v/t and a/t.
Understanding these will help in understanding constant acceleration.
A new one that I found 7/2/2011
These equations related, initial or starting velocity, u, the final velocity, v, the time taken, t, and the distance covered, s, tp the acceleration, a.
I just watched a video from a Lear 24 takeoff I did, 8 seconds to 80 kts, 10 to 100 kts and at 13 seconds from brake release, we were off the ground. The Falcon 20 in comparison, with CF700-2D2 engines, the typical time we monitor on takeoff is usually about 19-20 seconds to 100 knots. When we take the Falcon out of Toluca, Mexico, which is upwards of 2600m elevation, the ground roll is signifigantly longer during our 0 degree flap takeoffs to a Vr around 140ish kts. Altitude really bites into our performance and weight limits in them, not so much the Lear, but that's another story. The Lear is by far the most impressive airplane performance wise I have ever flown. I love hearing "Fly it like you stole it" ; ) Airliner-wise, the 757 gets up and goes and is my favorite to ride on.
Calculate the acceleration and distance covered in the 3 take-offs described in the piece
1knot = 0.514 m/s
Why do you think high altitude has an effect on the liftoff of the plane?
As far as you know the rule to be that acceleration leads to a change in velocity, correct ?
Velocity is speed in a given direction
So if the speed changes, so does the velocity,
also if the direction changes, so does the velocity,
acceleration is the rate of change of velocity, so the body has acceleration.
A body could spin about a point with a constant speed but still be accelerating.
The direction of the body is changing and therefore so too is it velocity,
If its velocity is changing then it is accelerating.
An accelerometer is included in many hand held devices, like iPhones and Wii remotes and soon will be in many more objects,
from the definition
Use simple maths to multiply across by t and rearrange to
The next equation we will use is concerned with distance, s = vt, but if the velocity changes then velocity must imply the average velocity
from the knowledge that distance is found by average velocity by the time, average velocity includes u & v (v= u + at)
squaring the original v=u + at formulae and then locating the formula for s above.
In Thorpe Park, UK there is a ride called the stealth,
it accelerates so quickly that they even advertise the ride by giving you the stats, see photo. Convert it into the metric system and calculate the average acceleration achieved in the 1st 2.3 seconds. If the rails were frictionless and no further force was applied how high in the sky could it go ?
To calculate acceleration of a moving body
Set up the air track at different angles.
By using a 'fin' of known length on top of the glider
and 2 light gates connected to seperate panels of the scalar timer
with each panel switched to 'gate'
measure the time that it takes the 'fin' to pass through each of the 'gates'
thus determine the average velocities for each of the gates
using theses as u & v and knowing the distance between them as s use
carry out drop 6 times each
take the LOWEST VALUE, usually we take the average .....
plot a graph of 2s Vs t2
s = ut + 1/2 at2
=> g = 2s/t2
A car starts travelling at 3 m/s and accelerates for 10 s at 5 m/s2. How far does it travel in 1 second, 5 seconds and 10 seconds.
When a body is rising then the bodies velocity actually becomes zero as the body stops rising and begins to fall.
u = x
v = 0