A car braked with a constant deceleration of 45ft/s^2 producing skid marks measuring 55 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? Please round the answer to the nearest hundredth.
Vo= ft/s
Vintial^2 - Vfinal^2= -2*acceleration*distance
Vfinal is zero. deacceleration is negative acceleration in the problem statement
thanks a bunch
To find the initial velocity (Vo) of the car when the brakes were first applied, we can use the formula:
Vinitial^2 - Vfinal^2 = -2 * acceleration * distance
Given:
Acceleration (deceleration) = -45 ft/s^2 (negative because deceleration slows down the car)
Distance = 55 ft
Vfinal = 0 ft/s (car comes to a stop)
Substituting these values into the formula:
Vinitial^2 - 0^2 = -2 * (-45 ft/s^2) * 55 ft
Simplifying the equation:
Vinitial^2 = 2 * 45 ft/s^2 * 55 ft
Vinitial^2 = 4950 ft^2/s^2
Taking the square root of both sides to solve for Vinitial:
Vinitial = √(4950 ft^2/s^2)
Now we can calculate Vinitial:
Vinitial ≈ 70.36 ft/s
Therefore, the car was traveling at approximately 70.36 ft/s when the brakes were first applied.