Variable Accelertaion Flashcards
How to variable acceleration
Basically
Going from displacement to velocity differentiate
Velocity to acceleration differentiate
Going from accerlwtion to velocity integrate
Velocity to displacement integrate
Bith WITH CONSTANT OF INTEGRATION
And can work this out using extra knowledge from question
For example = initslly it’s at rest = t 0 v 0
Or at s=3 it’s at rest, s=3 t=0 etc
Okay so find the times when particle 0
2) find the greatest displacement
3) find greatest speed )
Means making displacement = 0 and finding values
2) greatest displacement is when velocity BECOMES 0, because (this is a turning point on the displacement graph, so moving from highest displacement and going down ) (or moving from loosest and going up)
3) greatest speed is when acceleration 0, again turning point, going from either greatest to slowest or slowest and bepack up
So find turning point and sub in
But if interva, there could be a greater negative speed so find thst too
Bsdicslly draw graphs
Okay so did everything right but when it says find total distance what to do
Btw you have displacement time graph equation already, don’t need to integrate what you already differentiated😭
And so it’s not as easy as saying find displacement at 0 and and 4, that’s displamcent, Need DISTANCE
so yiu need to find out where it changes direction if it does, this is when v is 0, so find times
Then find displacement from 0 to thid and this to 4
And see how ,ich itsTraveller
Rest = velocity xero
Change direction = velocity change sign
Remember thwt draw graoh and see what to calculate, sometimes won’t need c because its just integration between limits!
Apparently integrate an e
IS THE SAME AS DIFFERNTIWTIJG
Have to remember
If it starts at something displamcent always 0 at t=0
Coming to rest is when equation for v = 0, you’ll have time again
Now can find distance
Also when t=0 displacement normally 0
When is greatest speed
When is greatest distances
Greatest v is when a =0
Greatest s is when v=0
When finding outndistance what to be wary of
Need to see when particle changes direction to make sure signs are there, because you need to integrate in psrts area of underneath and above
So always find when it vhanges direction (this is crossing if axis so when v=0)
And then see if it changed
Finally how to work out maximum everything d
Thid I’d the maximum point on Esch graoh which is when grsdient 0
Thus differentiate (which yiu prolly slrewdy hsve) snd = to 0
No need to think harf
For there to be a change in direction velocity must be ?
0 ar one point
So if no roots = never changed
If they say describe motion and given you a line what to say
If velocity negative it going away from starting point so say it moves left until v is 0
Then it moves back towards starting point and then say when it crosses this. It crosses this when displacement is 0, and then will accerlwtion towards the right side
Also say when v =0 it is monetarily stationary
Remember displamcent = 0 is not when V=0 it would be WHEN AREAS UP AND DOWN = 0 SO JUST PUT IN CALC
Okay yiu can now find greatest everythign, except speed? How to do this
The greatest VELOCITY is the MAXIMUM or MINIMUM point (which is either the greatest positbe or negative velocity) within a range
And to find this find minimum points .
This value is the greatest value between the stationary points !
So any value after or before the stationary points can have a greater negative velocity
And the greatest speed is just the maximum velocity here excluding any direction
So if yiu already found greatest velocity in a range
Check for any values out if the roots for time in your range
Test that
It should be other symbol = but this is your GREATEST SPEED!
Okay remember rules for logs etc
If ln and e next to Esch other it becomes 1 x power of ln don’t mess thst up
Like e ^ln 2 is just 2
And also the poeer rules is only for log snd ln
