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## Homework Statement

A jet plane comes in for a landing with a speed of

100 m/s, and its acceleration can have a maximum magnitude

of 5.00 m/s^2 as it comes to rest. (a) From the

instant the plane touches the runway, what is the minimum

time interval needed before it can come to rest?

## Homework Equations

Kinematics I suppose, but I'm trying to solve it with just calculus.

## The Attempt at a Solution

So my idea was that if the acceleration is constant at -5m/s^2 then I should be able to take the integral of this and get the velocity function. So what I end up with is

v(t) = - 5/2 (t^2) + 100

Solve for v(t) = 0 etc.

But the answer is wrong. It's supposed to be 20s.

Where is my logic flawed?