a bike first accelerates from 0m/s to 5.0m/s in 4.55, then continues at this constant speed for another 4.5s. what is the total distance traveled by the bike?
i think its 5 x 4.5 plus the initial 5 m= total displacement
To find the total distance traveled by the bike, we need to calculate the distance during each phase of its motion separately and then add them together.
First, let's calculate the distance during the acceleration phase. We can use the formula:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Since the bike accelerates from 0 m/s to 5.0 m/s in 4.55 s, the initial velocity is 0 m/s, the final velocity is 5.0 m/s, and the time is 4.55 s. We also know that the acceleration during this phase is:
acceleration = (final velocity - initial velocity) / time
Substituting the given values into the formula, we have:
acceleration = (5.0 m/s - 0 m/s) / 4.55 s
Now let's calculate the distance during the acceleration phase:
distance = (0 m/s * 4.55 s) + (1/2 * (5.0 m/s - 0 m/s) / 4.55 s * (4.55 s)^2)
Next, let's calculate the distance during the constant speed phase. Since the bike continues at a constant speed of 5.0 m/s for 4.5 s, the distance is simply:
distance = constant speed * time
distance = 5.0 m/s * 4.5 s
Finally, to find the total distance traveled by the bike, we add the distances from both phases:
total distance = distance during acceleration + distance during constant speed
total distance = [expression from the first calculation] + [expression from the second calculation]
If you substitute the values and calculate these expressions, you will get the total distance traveled by the bike.