# Kinematic Question

## Homework Statement

a vehicle is travelling at 25m/s. its breaks provide an acceleration of -3.75m/s^2. What is the drivers maximum reaction time is she is to avoid hitting an obstacle 95.0m away?

## Homework Equations

D=vi(t) +1/2a(t)^2
3. The Attempt at a Solution
D=95m
vi=25 m/s
a=-3.75m/s ^2
I plugged it into the equation D=vi(t) +1/2a(t)^2 and i got -2.02, which is obviously wrong

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gneill
Mentor

## Homework Statement

a vehicle is travelling at 25m/s. its breaks provide an acceleration of -3.75m/s^2. What is the drivers maximum reaction time is she is to avoid hitting an obstacle 95.0m away?

## Homework Equations

D=vi(t) +1/2a(t)^2

## The Attempt at a Solution

D=95m
vi=25 m/s
a=-3.75m/s ^2
I plugged it into the equation D=vi(t) +1/2a(t)^2 and i got -2.02, which is obviously wrong
In your attempt you've assumed that the braking begins immediately when there are still 95 m to the obstacle. This won't be the case. During the time it takes for the driver to react the vehicle continues to travel at its initial speed. Only after the driver reacts does the braking begin.

There are two intervals to be concerned about. The first interval is the period where the driver is deciding that she must brake and take action (the reaction time). The second is where the actual deceleration takes place. I suggest that you begin with the second interval and determine what the actual stopping distance is once the braking begins.

Your problem is that it doesn't take the entire 95 meters to stop. In other words, this person will have room left over. That's where you figure in the reaction time.

You'll need to use a formula that relates velocity, acceleration, and distance. Hint: the initial velocity is 25 m/s, and the final velocity is 0 m/s.

After you find the distance travelled during deceleration, then you know how much distance is left over. Then you find out how long it takes to travel that distance going 25 m/s, and you'll know how much time the driver has to react.