A car traveling 132 feet per second decelerates at a constant rate to 60 feet per second in three seconds.
A. what is the negative acceleration?
B. How long after the brakes are first applied will it take to come to a complete stop?
C. How far does it travel before coming to a stop from when the brakes are first applied?
change in velocity/change in time = (60-132)/3 = -24 ft/s^2
change in velocity = a t
0 - 132 = -24 t
t = 5.5 seconds to stop
d = Vi t + (1/2) a t^2
= 132(5.5) -.5(24)(5.5)^2
= 426 - 363 = 363 feet
To find the answers to these questions, we need to use the equations of motion.
A. To calculate the negative acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 132 feet per second, the final velocity is 60 feet per second, and the time is 3 seconds.
acceleration = (60 - 132) / 3 = -72 / 3 = -24 feet per second squared
Therefore, the negative acceleration is -24 feet per second squared.
B. To determine how long it takes for the car to come to a complete stop after the brakes are first applied, we need to find the time required for the velocity to reach zero. We can use the formula:
final velocity = initial velocity + (acceleration * time)
In this case, the initial velocity is 132 feet per second, the final velocity is 0 feet per second, and the acceleration is -24 feet per second squared.
0 = 132 + (-24 * time)
Simplifying the equation:
-132 = -24 * time
Dividing both sides by -24:
time = -132 / -24 = 5.5 seconds
Therefore, it will take 5.5 seconds for the car to come to a complete stop after the brakes are first applied.
C. To find the distance traveled before coming to a stop from when the brakes are first applied, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the initial velocity is 132 feet per second, the final velocity is 0 feet per second, the acceleration is -24 feet per second squared, and the time is 5.5 seconds.
distance = (132 * 5.5) + (0.5 * -24 * 5.5^2)
Simplifying the equation:
distance = 726 + (-264) = 462 feet
Therefore, the car will travel 462 feet before coming to a stop from when the brakes are first applied.