Well, let's crunch some numbers!
(a) To calculate the distance the car coasts before it stops, we can use the equation:
distance = (initial velocity)^2 / (2 * acceleration)
Given that the initial velocity is 75 km/h and the deceleration is 0.50 m/s², we need to convert the initial velocity to meters per second:
75 km/h = 75,000 meters/3,600 seconds = 20.83 m/s
Plugging the values into the equation, we have:
distance = (20.83 m/s)^2 / (2 * 0.50 m/s²)
distance = 866.07 meters
So the car coasts for approximately 866.07 meters before coming to a stop.
(b) To find the time it takes for the car to stop, we use the equation:
final velocity = initial velocity + (acceleration * time)
Since the final velocity is 0, we can rearrange the equation to solve for time:
time = (final velocity - initial velocity) / acceleration
Plugging in the values:
time = (0 m/s - 20.83 m/s) / (-0.50 m/s²)
time ≈ 41.66 seconds
So it takes approximately 41.66 seconds for the car to stop.
(c) To calculate the distance the car travels during the first five seconds, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time²)
For the first second:
distance = (20.83 m/s * 1s) + (0.5 * -0.50 m/s² * 1s²)
distance ≈ 20.83 meters
For the fifth second:
distance = (20.83 m/s * 5s) + (0.5 * -0.50 m/s² * 5s²)
distance ≈ 95.83 meters
So during the first second, the car travels approximately 20.83 meters, and during the fifth second, it covers around 95.83 meters.
Hope that answers your question with some mathematical comedy flair!