Kinematics - calculating acceleration

[TheronSimon]

Homework Statement

Jack is driving with a pail of water along a straight pathway at a steady 25 m/s when he passes Jill who is parked in her minivan waiting for him. When Jack is beside Jill, she begins accelerating at the rate of 4.0 x 10-3 m/s2 in the same direction that Jack is driving. How long does it take Jill to catch up to Jack?

Homework Equations

The Attempt at a Solution

I'm superbly and completely stumped by this, I really have no idea how to even begin solving this. If anyone could help that would be most appreciated!

 

[Mathoholic!]

If Jack is driving at a steady 25 m/s, then kinematics tell us that:

x(t)=25t

Now, Jill, initially at rest, starts accelerating at the rate of 4.0E-3 m/s², which results in:

x(t)=(1/2)(4.0E-3)t²

We are admitting that they both start their movement at the origin of (Oxy). You can now solve it for the same position (same x).

 

[TheronSimon]

so 25 = 2x10^-3 (t)^2
25= SQRT0.002
25= 0.0447
t= 25/0.0447
t= 559s
or t = 9.3 minutes

 

[tal444]

so 25 = 2x10^-3 (t)^2

25t, not 25. You must solve a quadratic equation.

 

[TheronSimon]

you lost me sorry :'(

 

[tal444]

x(t)=25t

x(t)=(1/2)(4.0E-3)t²

These are the two equations. You forgot take the t term in the first equation into account.

 

[TheronSimon]

so how about...
25 t^2 = .002 m/s^2 t^2 divide both sides by t^2
25 = .002 m/s^2 divide both by 0.002^2
so 25/ 0.002
so if we cancel out the m/s we are left with a sec so an answer of time of 12500 seconds or 3.47 hours.

 

[tal444]

Nice work, that is correct.

 

[Mathoholic!]

so how about...
25 t^2 = .002 m/s^2 t^2 divide both sides by t^2
25 = .002 m/s^2 divide both by 0.002^2
so 25/ 0.002
so if we cancel out the m/s we are left with a sec so an answer of time of 12500 seconds or 3.47 hours.

It's partiallly wrong, Jack's speed is constant (thus no acceleration!).

25t=(1/2)(4.0E-3)t² → (2.0E-3)t²-25t=0

You can either use the quadratic formula or cancel the product like so:

t=0 $\vee$ t=25/(2.0E-3)=12500s

You got the solution right but you used a wrong method as 25≠0.002.

 

[tal444]

Wow whoops, totally didn't see that xD