Final answer:
The car, decelerating at -2.0 m/s², traveled a total distance of 82.32 meters during the 4 seconds it was braking.
Step-by-step explanation:
When the brake of a car is pressed causing the car to slow down from a speed of 24.58 meters per second (m/s) at a rate of -2.0 m/s2 for a period of 4 seconds, we can determine the distance traveled by the car during this time using the equation of motion for uniformly accelerated motion, which is:
s = ut + ½ at2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.
Here, the initial velocity (u) is 24.58 m/s, acceleration (a) is -2.0 m/s2 which means the car is decelerating, and the time (t) is 4 s. Plugging in the values, we get:
s = (24.58 m/s)(4 s) + ½(-2.0 m/s2)(4 s)2.
First, calculate the first part of the equation: (24.58 m/s)(4 s) = 98.32 m. Then, calculate the second part: ½(-2.0 m/s2)(4 s)2 = -16 m.
Adding both parts together, we get the total distance traveled: 98.32 m - 16 m = 82.32 meters. Therefore, the car traveled 82.32 meters during the 4 seconds of braking.