At t=0 seconds, a ball is located at 1.9 m. At t=10 s,the position is 9.7 m . Calculate the position at t=5.8 s
To calculate the position of the ball at t=5.8 seconds, we can use the concept of linear interpolation. Linear interpolation allows us to estimate the value of an unknown quantity (in this case, the position) between two known values based on their linear relationship.
Here's how you can calculate the position at t=5.8 s:
1. Determine the time interval between the two known positions.
Δt = t₂ - t₁ = 10 s - 0 s = 10 s
2. Determine the position interval between the two known positions.
Δx = x₂ - x₁ = 9.7 m - 1.9 m = 7.8 m
3. Calculate the average velocity over the time interval using the formula:
v_avg = Δx / Δt
v_avg = 7.8 m / 10 s = 0.78 m/s
4. Determine the time difference between the desired time and the initial time.
Δt' = t' - t₁ = 5.8 s - 0 s = 5.8 s
5. Calculate the position at the desired time using the formula:
x' = x₁ + v_avg * Δt'
x' = 1.9 m + (0.78 m/s * 5.8 s) = 1.9 m + 4.524 m ≈ 6.424 m
Therefore, the position of the ball at t=5.8 seconds would be approximately 6.424 meters.