A car is traveling 10 m/s when the driver sees a dog in the road. The driver takes 0.7 s to react, then steps on the brakes and slows down at 3.0 m/s2. How far does the car go before it stops? Name the forces, their directions, and the distances involved in the following problem. Do not solve it mathematically.
3 seconds
To determine how far the car goes before it stops, we need to break down the problem and identify the different forces, their directions, and the distances involved.
1. Initial Velocity: The car is traveling at 10 m/s. This represents the initial speed of the car.
2. Reaction Time: The driver takes 0.7 s to react. During this time, the car continues moving at a constant velocity of 10 m/s.
3. Braking Force: Once the driver reacts, they step on the brakes. Upon doing so, the car decelerates at a rate of 3.0 m/s2. This deceleration is due to the braking force applied by the brakes.
4. Stopping Distance: The distance covered by the car before it comes to a complete stop is what we're looking to find.
To determine the stopping distance, we'll need to consider the following:
a. Distance covered during the reaction time: During the 0.7 s reaction time, the car continues moving at a constant velocity of 10 m/s. Therefore, the distance covered during the reaction time can be calculated using the formula: distance = initial velocity × time.
b. Distance covered due to deceleration: Once the driver applies the brakes, the car starts decelerating at a rate of 3.0 m/s2. To find the distance covered during the deceleration phase, we can use the formula: distance = (final velocity squared - initial velocity squared) / (2 × deceleration). Here, the final velocity is 0 m/s since the car comes to a stop.
Therefore, to find the total stopping distance, we'll add the distance covered during the reaction time and the distance covered due to deceleration.
It's important to note that although we are not solving the problem mathematically, following these steps will allow us to understand the forces, their directions, and the distances involved in determining the stopping distance of the car.