A biker first accelerates from 0.0 m/s to 6.0 m/s in 6 s, then continues at this speed for 5 s. What is the total distance traveled by the biker?
a = (6m/s)/(6s) = 1 m/s^2
under acceleration,
s = 1/2 at^2 = 1/2 * 1 * 6^2 = 18m
Now add that to the 6*5 m at constant speed
=48
Average acceleration of an object is the:
a = (6m/s)/(6s) = 1 m/s^2
under acceleration,
s = 1/2 at^2 = 1/2 * 1 * 6^2 = 18m
Now add that to the 6*5 m at constant speed
Why did the biker start pedaling really fast? Because they wanted to gain some momentum and speed things up!
To find the total distance traveled by the biker, we first need to calculate the distance traveled during the acceleration period and the distance traveled during the constant speed period.
1. Distance during acceleration:
The formula to calculate distance during acceleration is:
distance = initial velocity * time + 0.5 * acceleration * time^2
Given:
initial velocity (u) = 0 m/s
final velocity (v) = 6.0 m/s
time (t) = 6 s
Since the biker starts from rest (initial velocity = 0), the distance traveled during acceleration can be calculated as:
distance = 0.5 * (v - u) * t
distance = 0.5 * (6.0 m/s - 0 m/s) * 6 s
distance = 0.5 * 6.0 m/s * 6 s
distance = 18.0 m
2. Distance during constant speed:
The formula to calculate distance during constant speed is:
distance = speed * time
Given:
speed = 6.0 m/s
time = 5 s
The distance during constant speed can be calculated as:
distance = speed * time
distance = 6.0 m/s * 5 s
distance = 30.0 m
3. Total distance traveled:
To find the total distance traveled by the biker, we add the distances during acceleration and constant speed:
total distance = distance during acceleration + distance during constant speed
total distance = 18.0 m + 30.0 m
total distance = 48.0 m
Therefore, the total distance traveled by the biker is 48.0 meters.