calculate the acceleration of an object

ball on an inclined plane

you ever put a ball on a slant board??
what happened to the ball???
course tersevbut ball will move down with greater velocity. objects in motion changes dikatan accelerated pace.
so the acceleration is a change of pace every one unit of time. acceleration can be either increase or decrease the speed. accelerated if the object is said to increase the speed and otherwise slowed when the speed is reduced. acceleration twofold:

a. average acceleration

           an object moving with velocity fluctuations then the object has acceleration fluctuations as well. change in velocity divided by the time interval is called the average acceleration. the average acceleration formulated :

  a    =  ∆v / ∆t

           

     b. instantaneous acceleration

         change of pace in a very small time intervals called instantaneous acceleration. instantaneous acceleration is the limit of a change of pace for the time interval approaches zero.

a       =     lim    ∆v / ∆t

∆t-0

instantaneous acceleration can also be formulated as a derivative of the velocity.

a   =   dv / dt

to better understand, consider the following sample questions :

    motorcycle moved following equation as a function of time v = 3t²- 5t+4, with v in m / s and t in seconds. specify:

a. average acceleration when t = 2 and at t = 3

b. instantaneous acceleration at t = 4

settlement :

a. known equation of velocity v =  3t²- 5t + 4

    to find the average acceleration, use the formula : 

         a    =  ∆v / ∆t         a    = v₂ - v₁ / t₂ - t₁

     the velocity at t = 3 is :

      

     v₂ = 3t²- 5t + 4
         = 3 (3)² - 5 (3) + 4
         = 16 m/s

    and velocity at t = 2 is :

     v₁  = 3t²- 5t + 4
          = 3 (2)² - 5 (2) + 4
          = 6 m/s

so the average acceleration is :

        a   =  v₂ - v₁ / t₂ - t₁
             = 16 m/s - 6 m/s / 3s - 2s
             =  10 m/s²

b. instantaneous acceleration can be determined by using a differential calculation, thus :

    a  = dv / dt
       = d ( 3t²- 5t + 4 ) / dt
       = 6t - 5
       = 6 (4) - 5
       = 19 m/s²

we can now calculate the acceleration of an object with a simple formula .. :)