A bike first accelerates from 0.0m/s to 5.0m/s in 4.5s, then continues at this constant speed for another 4.5s. What is the total distance traveled by the bike?
a=5/4.5 m/s^2
distance=1/2 a*4.5^2 + (a*4.5)*4.5
solve for distance.
To find the total distance traveled by the bike, we need to calculate the distance covered during the acceleration phase and the distance covered during the constant speed phase, and then add them together.
1. Distance covered during the acceleration phase:
During this phase, the bike starts from rest (0.0 m/s) and accelerates to a final velocity of 5.0 m/s in 4.5 seconds. We can use the formula for distance covered during constant acceleration:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the initial velocity is 0.0 m/s, the final velocity is 5.0 m/s, and the time is 4.5 seconds. Since we are given the final velocity but not the acceleration, we need to calculate it first.
The acceleration can be found by using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (5.0 m/s - 0.0 m/s) / 4.5 s = 1.1 m/s^2
Using this value, we can now calculate the distance covered during acceleration using the formula:
distance = (0.0 m/s * 4.5 s) + (0.5 * 1.1 m/s^2 * (4.5 s)^2)
distance = 0.0 m + 0.5 * 1.1 m/s^2 * 20.25 s^2
distance = 0.0 m + 11.025 m
distance = 11.025 m
2. Distance covered during the constant speed phase:
During this phase, the bike maintains a constant speed of 5.0 m/s for 4.5 seconds. The distance covered is simply the product of the constant speed and the time:
distance = speed * time
distance = 5.0 m/s * 4.5 s
distance = 22.5 m
Now, we can find the total distance traveled by adding the distances covered during the acceleration and constant speed phases:
total distance = distance during acceleration + distance during constant speed
total distance = 11.025 m + 22.5 m
total distance = 33.525 m
Therefore, the total distance traveled by the bike is 33.525 meters.