Truck vs Tree (first week physics woes)

[youagain]

1. The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with an acceleration of -5.60 m/s2 for 4.20s making skid marks 62.4m long that end at the tree. With what speed does the truck strike the tree?

Homework Equations

I'm guessing that I have to use V_f²-V_o²=2as?

I'm really not sure... I've been staring at this problem for hours, is It a trick question? Does it even hit the tree?

 

[willem2]

You need

$$x = x_0 + v_0 t + (1/2) a t^2$$

you know everyting except for the initial speed.

 

[youagain]

Man i am defenitly going to need to work on knowing which formulas are for which... ummm using that...x=v_o²+1/2at²
v_o²= x-1/2at²
So v_o = square root x-1/2at²square root of 62.4-(-5.6x4.2²)/2= 10.573

So he hits the tree at 10.58 m/s?EDIT: Wait did I miss out a t? let me try that again...

 

[youagain]

x-(1/2)at²/t=v_o


62.4-(1/2)-5.6x4.2²
/4.2

=

26.617 m/s



So that's his initial speed right?

I still don't understand how to get his final speed?

 

[youagain]

Wait V=V_o+at

so 26.617+(-5.6x4.2) = 3.097

does he hit the tree at 3.097 m/s?

 

[cristo]

Be careful with your rearranging. If

$$x=v_0t+\frac{1}{2}at^2$$

then

$$v_0=\frac{1}{t}\Big(x-\frac{1}{2}at^2\Big)=\frac{x}{t}-\frac{1}{2}at$$

 

[youagain]

I think its just my formating making it look wrong? is 26.617 m/s the right answer?