Lab 3. Unconstant Acceleration

Today, we are going to find the relations between unconstant acceleration a and velocity v, and position x.

Example: There is a 5000kg elephant who has a constant velocity 25 m/s at the beginning. and the elephant has a rocket who is (1500 + 20t)kg on his back. Suddenly, the rocket starts to fire and gives 8000N to decrease the elephant.

There are calculation and equations :

From the equation of velocity,  we could know the graph of velocity:

Then, we can imagine △t is small enough,..

like the pictures, we could have some variables:
                                              when △t = 0.1s,

set t starts from 0.
t = t + △t

a = F/m = -400/(325 - t)      

△v = △a * △t = (a0 + a1)*△t/2        (a0 = -1.23 m/s^2)

v = v0 + △v = 25m/s + △v

v-avg = (v0 + v)/2

△x = v-avg * △t

x = x0 + △x



Open the excel, and input the data which we already know. and then we will have many data from t = 0s and time interval is 0.1s.  Here is the picture of data.

there is a v = 0 when t is between 19.6s and 19.7s,
right now, we can test our equations.
when t = 19.6s:

after calculated, we got almost same result with the data on excel.

For a unconstant acceleration problem, we can treat the graph of acceleration as a straight when we choose a time interval as small enough. then we could calculate anything we want.