A car is originally traveling at 15.0 meters per second on a straight horizontal road.The driver applies the brakes causing the car to decelerate at 4.00 meters per second ^2 until it comes to a rest. Determine the cars stopping distance
To determine the car's stopping distance, we need to calculate the distance it travels while decelerating until it comes to a rest.
The formula to calculate the stopping distance is:
Stopping distance = (initial velocity squared) / (2 * deceleration)
Given:
Initial velocity (u) = 15.0 m/s
Deceleration (a) = -4.00 m/s^2 (negative sign indicates deceleration)
Substituting the values into the formula, we have:
Stopping distance = (15.0 m/s)^2 / (2 * -4.00 m/s^2)
Now let's solve this equation step by step:
1. Calculate the square of the initial velocity:
(15.0 m/s)^2 = 225.0 m^2/s^2
2. Multiply the square of the initial velocity by 2 times the deceleration:
225.0 m^2/s^2 / (2 * -4.00 m/s^2) = -56.25 m
Since distance can't be negative, we take the absolute value of the result, which gives us the car's stopping distance:
Stopping distance = |-56.25 m| = 56.25 meters
Therefore, the car's stopping distance is 56.25 meters.