If your car goes from 0 mi/h to 70 mi/h in 8 s, what is your average acceleration?
Answer in units of miles/(hours x seconds
).
To find the average acceleration, we need to determine the change in velocity (Δv) and the time interval (Δt) over which the change occurs.
Given:
Initial velocity (v₀) = 0 mi/h
Final velocity (v) = 70 mi/h
Time (t) = 8 s
The formula to calculate average acceleration is:
Average acceleration (a) = Δv / Δt
To find Δv, we subtract the initial velocity from the final velocity:
Δv = v - v₀
Δv = 70 mi/h - 0 mi/h
Δv = 70 mi/h
Δt is already given as 8 seconds.
Now, we can substitute the values into the average acceleration formula:
a = Δv / Δt
a = 70 mi/h / 8 s
To express the answer in the desired units of miles/(hours x seconds), we need to convert the time unit from seconds to hours:
1 hour = 60 minutes
1 minute = 60 seconds
So, we can convert 8 seconds to hours:
8 s * (1 min / 60 s) * (1 hour / 60 min) = 8/3600 hours (simplified)
Now we can rewrite the average acceleration using the desired units:
a = 70 mi/h / (8/3600 hours)
To divide by a fraction, we multiply by its reciprocal:
a = 70 mi/h * (3600/8 hours)
Simplifying the expression:
a = 31,500 mi/(8 hours)
Therefore, the average acceleration is 31,500 mi/(8 hours).