A car is traveling at `45 m/s` . A dog runs out in front of the car. It decelerates to zero with a constant rate of `20 m/s^2` . How long it takes a car stop?

Expert Answers

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First, let us set-up the system, and identify the variables:

The initial velocity, `v_i` , is `45 m/s` .

The final velocity, `v_f` , is `0 m/s` .

The acceleration,`a` , is `-20 m/s^2` . Note the negative sign to denote decceleration.

We want to find `t` , the time it takes, given the acceleration, to reach the final velocity from the initial velocity -- essentially, how long before the car stops.

The formula that we need is as follows:

`v_f = v_i + at`

Isolating `t` ,

`t = (v_f - v_i)/a`

Then, we simply plug-in the values:

`t = (0 - 45)/(-20) = 2.25`

That is, it takes 2.25 seconds before the car stops.

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