A man ruins at a velocity of 4.5 m/s for 15 minutes. When

going up an increasingly steep hill, he slows down at a constant rate of 0.05 m/? for 90.0 seconds and comes to a stop. How far did he run?

1 answer

To find the distance the man ran, we need to find the total distance traveled during the initial velocity and the distance traveled during the deceleration.

The initial velocity is 4.5 m/s, and the time for which he ran at this velocity is 15 minutes. We need to convert minutes to seconds:
15 minutes * 60 seconds/minute = 900 seconds

The distance traveled during the initial velocity can be calculated using the formula:
distance = velocity * time
distance = 4.5 m/s * 900 seconds = 4050 meters

Now let's find the distance traveled during the deceleration. The deceleration rate is -0.05 m/s², and the time for which he decelerates is 90.0 seconds. We need to calculate the final velocity using the formula:
final velocity = initial velocity + (acceleration * time)
final velocity = 4.5 m/s + (-0.05 m/s² * 90.0 seconds) = 4.5 m/s - 4.5 m/s = 0 m/s

Now we can calculate the distance traveled during deceleration using the formula:
distance = (initial velocity + final velocity) / 2 * time
distance = (4.5 m/s + 0 m/s) / 2 * 90.0 seconds = 2.25 m/s * 90.0 seconds = 202.5 meters

The total distance traveled is the sum of the distance during the initial velocity and the distance during deceleration:
total distance = 4050 meters + 202.5 meters = 4252.5 meters

Therefore, the man ran a total distance of 4252.5 meters.