To calculate average acceleration from distance traveled and time taken, you need to know the initial velocity (v₀), final velocity (v), and the time taken (t). If you have the initial and final positions instead of velocities, you can calculate the velocities using the formula v = ∆s / t, where ∆s is the change in position.
The formula to calculate average acceleration is:
Average acceleration (a) = (v - v₀) / t
Here's an example to illustrate the calculation:
Suppose a car starts from rest (v₀ = 0 m/s) and reaches a velocity of 30 m/s in 5 seconds (t = 5 s). To find the average acceleration:
v = 30 m/s t = 5 s
Average acceleration (a) = (30 m/s - 0 m/s) / 5 s = 6 m/s²
Therefore, the average acceleration of the car during this 5-second interval is 6 meters per second squared (m/s²).