a car is approaching a traffic light at 25m/s when it turns red. The driver takes 1 second to react and put his foot on the brake pedal, after which the car decelerates at 2m/s^2. find the distance needed for the car to come to stop after the light turns red
The distance that the car moves while decelerating is
X = Vo^2/(2a) = 625/4 = 156.3 feet
An additional distance of (25 m/s)*1 s = 25 m is travelled before the brakes are applied.
The sum of the two is the stopping distance
To find the distance needed for the car to come to a stop after the light turns red, we need to consider the initial velocity, the deceleration, and the time it takes for the driver to react.
Let's break down the problem step by step:
1. Find the distance covered during the reaction time:
The car is approaching the traffic light at a velocity of 25 m/s. The driver takes 1 second to react, during which time the car continues moving forward at the same velocity. Therefore, the distance covered during the reaction time is given by:
Distance = Velocity * Time
= 25 m/s * 1 s
= 25 meters
So, during the reaction time, the car covers a distance of 25 meters.
2. Find the distance covered during the deceleration:
After the driver reacts, the car starts decelerating at a rate of 2 m/s^2 until it comes to a stop (zero velocity). We can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity (0 m/s), u is the initial velocity (25 m/s), a is the deceleration (-2 m/s^2), and s is the distance covered.
Rearranging the equation, we get: s = (v^2 - u^2) / (2a)
Plugging in the values, we have:
s = (0^2 - 25^2) / (2 * -2)
= -625 / -4
= 156.25 meters
So, the car covers a distance of 156.25 meters during the deceleration.
3. Add the distances covered during the reaction time and deceleration:
Total Distance = Distance during reaction time + Distance during deceleration
= 25 meters + 156.25 meters
= 181.25 meters
Therefore, the car needs a distance of 181.25 meters to come to a stop after the light turns red.