Final answer:
The average acceleration of the car during braking is -10 m/s², and the car travels a distance of 20 meters while the brakes are applied.
Step-by-step explanation:
A car is traveling at 20 m/s when the driver applies the brakes and it takes 2 seconds for the car to come to a stop. To calculate the average acceleration of the car during braking, we use the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. The car comes to a stop, which means that the final velocity (v_f) is 0 m/s, and the initial velocity (v_i) is 20 m/s. Therefore, the change in velocity (Δv) is v_f - v_i = 0 m/s - 20 m/s = -20 m/s. The time it takes to stop (Δt) is 2 seconds. So the average acceleration is Δv / Δt = -20 m/s / 2 s = -10 m/s². Note that the acceleration is negative because it is in the opposite direction to the car's motion (deceleration).
To find out how far the car travels while the brakes are being applied, we can use the kinematic equation s = v_i * Δt + 0.5 * a * (Δt)², where s is the displacement. Plugging in the values we have s = 20 m/s * 2 s + 0.5 * (-10 m/s²) * (2 s)² = 40 m - 20 m = 20 m. Therefore, the car travels 20 meters while the brakes are applied.