A particle moves according to the equation x= (10 m/s^2)t^2 where x is in meters and t is in seconds.
a. Find the average velocity for the time interval from t1= 2.38 s to t2= 4.3 s.
Answer in units of m/s.
b. Find the average velocity for the time interval from t1= 2.38 s to t3= 2.48 s.
Answer in units of m/s.
To find the average velocity, we need to calculate the change in position (Δx) divided by the change in time (Δt).
a. For the time interval from t1 = 2.38 s to t2 = 4.3 s:
Step 1: Calculate the change in position (Δx) by substituting the values of t1 and t2 into the position equation:
Δx = x2 - x1
Δx = [(10 m/s^2)(4.3 s)^2] - [(10 m/s^2)(2.38 s)^2]
Step 2: Calculate the change in time (Δt) by subtracting t1 from t2:
Δt = t2 - t1
Δt = 4.3 s - 2.38 s
Step 3: Calculate the average velocity by dividing Δx by Δt:
Average velocity = Δx / Δt
b. For the time interval from t1 = 2.38 s to t3 = 2.48 s:
Step 1: Calculate the change in position (Δx) by substituting the values of t1 and t3 into the position equation:
Δx = x3 - x1
Δx = [(10 m/s^2)(2.48 s)^2] - [(10 m/s^2)(2.38 s)^2]
Step 2: Calculate the change in time (Δt) by subtracting t1 from t3:
Δt = t3 - t1
Δt = 2.48 s - 2.38 s
Step 3: Calculate the average velocity by dividing Δx by Δt:
Average velocity = Δx / Δt
By following these steps, you can find the average velocities for both time intervals. Make sure to perform the calculations to obtain the final answers in units of m/s.
To find the average velocity for a given time interval, you need to calculate the displacement and divide it by the time interval.
a. For the time interval from t1 = 2.38 s to t2 = 4.3 s, we can find the displacement by subtracting the position at t1 from the position at t2.
At t1 = 2.38 s, x1 = (10 m/s^2) * (2.38 s)^2 = 57.2256 m.
At t2 = 4.3 s, x2 = (10 m/s^2) * (4.3 s)^2 = 184.43 m.
The displacement, Δx, is given by Δx = x2 - x1 = 184.43 m - 57.2256 m = 127.2044 m.
The time interval, Δt, is given by Δt = t2 - t1 = 4.3 s - 2.38 s = 1.92 s.
Now, we can calculate the average velocity by dividing the displacement by the time interval:
Average velocity = Δx / Δt = 127.2044 m / 1.92 s ≈ 66.28 m/s.
So, the average velocity for the time interval from t1 = 2.38 s to t2 = 4.3 s is approximately 66.28 m/s.
b. For the time interval from t1 = 2.38 s to t3 = 2.48 s, we can again find the displacement by subtracting the position at t1 from the position at t3.
At t1 = 2.38 s, x1 = (10 m/s^2) * (2.38 s)^2 = 57.2256 m.
At t3 = 2.48 s, x3 = (10 m/s^2) * (2.48 s)^2 = 62.0416 m.
The displacement, Δx, is given by Δx = x3 - x1 = 62.0416 m - 57.2256 m = 4.816 m.
The time interval, Δt, is given by Δt = t3 - t1 = 2.48 s - 2.38 s = 0.1 s.
Now, we can calculate the average velocity by dividing the displacement by the time interval:
Average velocity = Δx / Δt = 4.816 m / 0.1 s = 48.16 m/s.
So, the average velocity for the time interval from t1 = 2.38 s to t3 = 2.48 s is 48.16 m/s.