# Multi Phase Kinematics Problem

1. Sep 18, 2011

### canadiankid

1. I have been given the total distance (100m) and the total time (9.780s) as well as a speed (11.7m/s) at t1 and a final speed (10.5m/s) at the end of the given time (9.780s). The initial velocity is zero at t=0. Acceleration is constant. I am not asking for the answer, just an algebra based formula or series of formulas to lead me in the right direction (question was on a midterm two years ago), since i do not have d, a or t for t1. I need to find:
a)What is the duration of the first acceleration phase? (t=0 to t1)
b)What is the constant acceleration during the first phase?
c)What is the constant negative acceleration during the second phase? (t1 to 9.780s)

Im not sure what any relevant equations are as I cannot find one that doesnt require at least two of a,d or t.

I calculated the average acceleration from t=0 to t=9.780s (a=20.4499m/s2) but that seems useless to me. I drew the acceleration, velocity (labelled this one) and position graphs to re-enforce the broader concept.

Thanks in advance for the help!!

2. Sep 18, 2011

### PeterO

You need to make use of the formula s = t * (u+v)/2
Here
s = displacement (perhaps what you called d?)
u = initial velocity
v = final velocity
t = time

Translated to English that formula reads displacement equals time by average velocity.

For the first phase u = 0, v = 11.7, t = t1
For the second phase u = 11.7, v = 10.5, t = 9.78 - t1

The total of those two displacements = 100

This will enable you to solve for t1, and once you have that it should all be easy

3. Sep 18, 2011

### canadiankid

Ah yes it is a system of equations... I always over think those. Thank you very much!

And yes I did you d for displacement, however you are more correct as d would represent distance, not displacement.

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