Final answer:
Alayah's acceleration is calculated by converting her speed from miles per hour to meters per second, finding the change in velocity, and dividing by the time taken. Her acceleration is 0.2225 meters per second squared.
Step-by-step explanation:
The subject of your question is Physics, and it involves concepts typically taught at the High School level. To find Alayah's acceleration, we need to use the formula for acceleration, which is a change in velocity divided by the time over which the change occurs. Alayah increased her speed from 7 miles per hour to 9 miles per hour in 4 seconds.
To calculate the acceleration, we first convert the speeds from miles per hour to meters per second:
1 mile = 1609.34 meters
1 hour = 3600 seconds
The initial velocity (v_i) is 7 miles/hour × 1609.34 meters/mile / 3600 seconds/hour = 3.13 m/s
The final velocity (v_f) is 9 miles/hour × 1609.34 meters/mile / 3600 seconds/hour = 4.02 m/s
The change in velocity (Δv) is v_f - v_i = 4.02 m/s - 3.13 m/s = 0.89 m/s. The time (Δt) over which this change occurred is 4 seconds.
Acceleration (a) can now be calculated:
a = Δv / Δt = 0.89 m/s / 4 s = 0.2225 m/s²
Therefore, Alayah's acceleration when she sees the finish line is 0.2225 meters per second squared.