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 = (V-Vo)/t = 5-0)/4.5 = 1.11 m/s^2.

d1 = 0.5a*t^2 = 0.5*1.11*4.5^2=11.25 m.

d2 = 5m/s * 4.5s = 22.5 m.

D = d1 + d2 = 11.25 + 22.5 = 33.75 m.

A+B

To find the total distance traveled by the bike, we need to calculate the distance during acceleration and the distance during constant speed.

Since the bike initially accelerates from 0.0m/s to 5.0m/s in 4.5s, we can use the formula:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Given:
Initial velocity (u) = 0.0 m/s
Final velocity (v) = 5.0 m/s
Time (t) = 4.5 s

Plugging in the values:

distance = (0.0 * 4.5) + (0.5 * acceleration * 4.5^2)

We can rearrange the equation to solve for the acceleration:

v = u + at

5.0 = 0.0 + a * 4.5

a = (5.0 - 0.0) / 4.5

a = 1.111 m/s^2

Now we can substitute the value of acceleration back into the distance equation:

distance = (0.0 * 4.5) + (0.5 * 1.111 * 4.5^2)

distance = 0.0 + (0.5 * 1.111 * 4.5 * 4.5)

distance = 0.0 + (0.5 * 1.111 * 20.25)

distance = 0.0 + 11.40375

distance = 11.40375 m (rounded to 2 decimal places)

So the distance covered during acceleration is 11.40 m.

Next, during the constant speed phase, the bike continues to travel at a speed of 5.0 m/s for 4.5 s.

distance = speed * time

distance = 5.0 m/s * 4.5 s

distance = 22.5 m

So the distance covered during constant speed is 22.5 m.

Finally, to find the total distance traveled by the bike, we can sum up the distances from the two phases:

total distance = distance during acceleration + distance during constant speed

total distance = 11.40 m + 22.5 m

total distance = 33.90 m

Therefore, the total distance traveled by the bike is 33.90 meters.

To find the total distance traveled by the bike, we need to calculate the distance traveled during each phase (acceleration and constant speed) and then add them together.

Phase 1: Acceleration from 0.0m/s to 5.0m/s in 4.5s
During this phase, we can use the formula to calculate the distance traveled during acceleration:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Given:
initial velocity (u) = 0.0 m/s
final velocity (v) = 5.0 m/s
time (t) = 4.5 s

Since the bike starts from rest, the initial velocity (u) is 0.0 m/s. Therefore, the formula simplifies to:

distance = 0.5 * acceleration * time^2

We need to find the acceleration (a) during this phase. The acceleration can be calculated using the formula:

acceleration = (change in velocity) / time

change in velocity = final velocity - initial velocity
change in velocity = 5.0 m/s - 0.0 m/s = 5.0 m/s

acceleration = (5.0 m/s) / (4.5 s) = 1.11 m/s^2 (rounded to two decimal places)

Substituting the values into the distance formula:

distance = 0.5 * 1.11 m/s^2 * (4.5 s)^2
distance ≈ 10.01 m

Phase 2: Constant speed of 5.0m/s for 4.5s
During this phase, since the speed is constant, the distance traveled can be calculated by multiplying the speed by the time:

distance = speed * time
distance = 5.0 m/s * 4.5 s
distance = 22.5 m

Total distance traveled:
To find the total distance, we add the distances obtained from each phase:

total distance = distance during acceleration + distance during constant speed
total distance = 10.01 m + 22.5 m
total distance ≈ 32.51 m

Therefore, the total distance traveled by the bike is approximately 32.51 meters.