Kinematics Problem: Solve for a (Vi=0, Vf=Vmax)

[shawli]

Homework Statement

I've attempted this problem for just Laura so far.

t₁ = 2.00s
t₂ = 10.4s - 2.00s = 8.40s

v_i = 0.0m/s
v_f at the end of 2.00s = v_max

For her displacement I have a little diagram:

|------------------|---------------------------|
...x.....x_f = 100 - x...

where the split between the two sections occurs at whatever x is after 2.00s.

a=? for the initial time interval from 0.00s to 2.00s.
a=0 from 2.00s to 10.4s.

Homework Equations

For constant velocity: x_f = x_i + v*t

For constant acceleration:

The Attempt at a Solution

From t=0.00 to t=2.00:

(using eq'n 2.15, where x_f=x, x_i=0, v_xi=0, and t₁ = 2.00)

x = 0.5 * v * t₂
x = 0.5 *v*2.00
x = v (?)


From t=2.00 to t=10.4:

(using constant velocity equation, where x_i=0, and x_f = 100 - x, and t₂=8.40)

100 - x= v * t₂
100 - x = v*8.40


And basically when I equate the two equations I don't get the right answer (which is a=5.32m/s...). Help!

 

[Delphi51]

All your work looks correct - I don't know how you missed the final answer. You have that the distances for the two parts are v and 8.4*v.
So v + 8.4*v = 100. That works out to v = 10.6.
a = Δv/Δt = 10.6/2 = 5.3 m/s².

 

[shawli]

God Da-...Ugghh.

Well then. Frustrating, but I guess it feels good to know I had it all along haha.

Thank you :)