Instantaneous Speed & Acceleration: Equations Explained

[lostfan176]

how do you find instantaneous speed and instantaneous acceleration. is there an equation?

 

[bob1182006]

instantaneous acceleration is the limit of change of velocity divided by change of time as the change of time goes to 0. Which is the derivative of velocity.

Usually you are given an equation for velocity or position and you take derivatives to get an equation for acceleration/velocity.

Instantaneous speed would be instantaneous velocity which is the derivative of the equation of the positioin of a particle without any direction.

So if you're given x=a+bt+ct^2 and asked for instanatenous velocity/acceleration at time t=1 you can just do:

dx/dt=b+2ct =v v(1) = b+2c
dv/dt=2c = a a(1)=2c

 

[lostfan176]

In Fig. P18, what was the car's instantaneous acceleration at t = 3.0 s? What was its instantaneous acceleration at t = 2.25 s?

so how would i use that equation to find the solution i don't know what the variables stand for

 

[bob1182006]

ok well the derivative is also the slope of the line tangent to the graph of a function at time t.

So looking at your graph what is the slope (i.e. change in y/x) at time t=4?

Edit: ok just saw the graph again o.o looked different before ><.

Hm...ok what does the acceleration do to velocity? velocity describes how fast position changes. so acceleration describes?

 

[lostfan176]

rate of change of velocity but like where do u plug in the numbersEDIT: oooo i get since at 3 sec its at a stand still its 0 but how do you do the 2.25 one?