While driving her new fuel efficient mini-car, Zelda changes her velocity from 22 km/h [forward] to 85 km/h [forward] while driving 2.0 × 102 m. What is her average acceleration ?
22,000/3600 = 6.11 m/s
85 000/3600 = 23.61 m/s
average speed during acceleration = 14.86 m/s
t = distance/speed = 200/14.86 = 13.46 s
a = speed change/time = 17.5/13.46 = 1.3 m/s^2
To calculate the average acceleration, we need to use the formula:
Average acceleration = (final velocity - initial velocity) / time
However, the given information does not include the time taken to change the velocity. We only have the distance traveled. To find the time, we can use the equation of motion:
Distance = (initial velocity + final velocity) / 2 * time
Since we know the distance traveled (2.0 × 10^2 m) and initial velocity (22 km/h), we can rearrange the equation to solve for time:
time = 2 * Distance / (initial velocity + final velocity)
Converting the velocities to meters per second (m/s) for consistency:
initial velocity = 22 km/h = (22 * 1000) / 3600 m/s
final velocity = 85 km/h = (85 * 1000) / 3600 m/s
Plugging in the values:
time = 2 * (2.0 × 10^2) / ((22 * 1000 / 3600) + (85 * 1000 / 3600))
Simplifying the calculation:
time = 2 * (2.0 × 10^2) / ((22 * 1000 + 85 * 1000) / 3600)
time = 2 * (2.0 × 10^2) / (107 * 1000 / 3600)
time = 2 * (2.0 × 10^2) / 29.4444
time ≈ 13.62 seconds
Now that we have the time, we can calculate the average acceleration using the initial and final velocities:
Average acceleration = (final velocity - initial velocity) / time
Average acceleration = ((85 * 1000) / 3600 - (22 * 1000) / 3600) / 13.62
Average acceleration ≈ (236.11 - 61.11) / 13.62
Average acceleration ≈ 175 / 13.62
Average acceleration ≈ 12.85 m/s²
Therefore, Zelda's average acceleration is approximately 12.85 m/s².