Final answer:
Acceleration is calculated by dividing the change in velocity by the change in time. For example, a train going from 0 to 30.0 km/h in 20 seconds has an acceleration of 0.4165 m/s².
Step-by-step explanation:
To find acceleration, we need to know the change in velocity (Δv) and the change in time (Δt). Acceleration (a) can be calculated using the formula a = Δv/Δt. Let's create a word problem to illustrate this concept:
Suppose a train starts from rest and reaches a speed of 30.0 km/h in 20.0 seconds. How can we find the train's acceleration?
First, convert the final velocity to meters per second (30.0 km/h ≈ 8.33 m/s since 1 km/h is approximately 0.2778 m/s).
Since the train starts from rest, the initial velocity (vo) is 0 m/s.
Calculate the change in velocity (Δv), which is final velocity (vₒ) minus initial velocity (vo): Δv = 8.33 m/s - 0 m/s = 8.33 m/s.
Identify the change in time (Δt) as 20.0 seconds.
Finally, calculate the acceleration using the formula a = Δv/Δt = 8.33 m/s ÷ 20.0 s = 0.4165 m/s².
Thus, the train's acceleration is 0.4165 m/s².