# Truck vs Tree (first week physics woes)

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 Vf2-Vo2=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?

You need

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

you know everyting except for the initial speed.

Man i am defenitly going to need to work on knowing which formulas are for which... ummm using that...

x=vo2+1/2at2

vo2= x-1/2at2

So vo = square root x-1/2at2

square 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...

x-(1/2)at2/t=vo

62.4-(1/2)-5.6x4.22
/4.2

=

26.617 m/s

So thats his initial speed right?

I still dont understand how to get his final speed?

Wait V=Vo+at

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

does he hit the tree at 3.097 m/s?

cristo
Staff Emeritus
Be careful with your rearranging. If

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

then

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

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