A car is initially travelling at 30 m/s, which is above the speed limit. The driver sees a speed limit trap ahead and applies the brakes for 5 seconds, causing the car to slow down by 2m/s every second while the brakes are on.
–How far does a car travel whilst the brakes are
being applied?
a = -2 m/s^2
v = Vi - 2 t
v = 30 - 2*5 = 20 at the end
so average v = 25 m/s
25*5 = 125 meters
To calculate the distance the car travels while the brakes are being applied, we can use the formula for distance:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time^2
In this case, the initial velocity is 30 m/s, the time the brakes are applied is 5 seconds, and the acceleration is -2 m/s^2 (since the car is slowing down).
Plugging in these values, we get:
Distance = 30 m/s * 5 s + 0.5 * (-2 m/s^2) * (5 s)^2
= 150 m - 0.5 * 2 m/s^2 * 25 s^2
= 150 m - 0.5 * 2 m/s^2 * 625 m^2
= 150 m - 0.5 * 2 * 625 m
= 150 m - 0.5 * 1250 m
= 150 m - 625 m
= -475 m
Therefore, the car travels a distance of 475 meters while the brakes are being applied.
To determine the distance traveled by the car while the brakes are being applied, we need to calculate the deceleration, the time the brakes are applied, and apply the appropriate formula for distance.
First, let's calculate the deceleration:
The car is slowing down by 2 m/s every second while the brakes are on. Since the initial velocity is 30 m/s and the final velocity is 0 m/s (since the car comes to a stop), we can calculate the average deceleration using the formula:
Acceleration (deceleration) = (Final Velocity - Initial Velocity) / Time
Deceleration = (0 m/s - 30 m/s) / 5 s
Deceleration = -30 m/s / 5 s
Deceleration = -6 m/s^2
Now that we have the deceleration, we can use the equation of motion to find the distance traveled while the brakes are applied:
Distance = (Initial Velocity * Time) + (0.5 * Acceleration * Time^2)
Distance = (30 m/s * 5 s) + (0.5 * (-6 m/s^2) * (5 s)^2)
Distance = 150 m - 75 m
Distance = 75 meters
Therefore, the car travels 75 meters while the brakes are being applied.