A child trying to catch an ice-cream truck (kinematics question)

[Sean1218]

Homework Statement

A child is running at her maximum speed of 4.0 m/s to catch an ice-cream truck, which is stopped at the side of the road. When the child is 20 m from the truck, the ice-cream truck starts to accelerate away at a rate of 1.0 m/s^2. Does the child catch the truck?

Homework Equations

d = vt
d = v1t + 1/2at^2 + 20

The Attempt at a Solution

4t = 1/2(1)t^2 + 20
0 = 1/2t^2 - 4t + 20

I can't factor normally, and I get error (square root of negative number) when I use quadratic equation. What is this telling me? That the child doesn't catch the ice-cream truck? Why? or did I do something wrong?

 

[quenderin]

There's no real solution to t: so the child never catches up. You're right. Another way to think about this is to find out how far apart they are when the ice-cream truck hits 4 m/s (if the child hasn't caught up at this stage, then she'll never catch up).

 

[The legend]

you have done the sum right!
Your negative square root indicates the child doesn't reach the truck...poor guy, i pity him