A bike first accelerates from 0.0 m/s to 4.5 m/s in 4.5 s, then continues at this constant speed for another 4.0 s. What is the total distance traveled by the bike?
To find the total distance traveled by the bike, we need to break down the motion into two parts: the acceleration phase and the constant speed phase.
First, let's calculate the distance covered during the acceleration phase.
We know the initial velocity (u) is 0.0 m/s, the final velocity (v) is 4.5 m/s, and the time taken (t) is 4.5 s. We can use the formula:
Distance (s) = (v - u) * t
Substituting the values, we have:
Distance (acceleration phase) = (4.5 m/s - 0.0 m/s) * 4.5 s
= 4.5 m/s * 4.5 s
= 20.25 m
Now let's calculate the distance covered during the constant speed phase.
The bike moves at a constant speed of 4.5 m/s for 4.0 seconds. So the distance covered is:
Distance (constant speed phase) = speed * time
= 4.5 m/s * 4.0 s
= 18.0 m
To find the total distance traveled by the bike, we sum up the distances covered during the acceleration and constant speed phases:
Total distance = Distance (acceleration phase) + Distance (constant speed phase)
= 20.25 m + 18.0 m
= 38.25 m
Therefore, the total distance traveled by the bike is 38.25 meters.