Final answer:
To find the average velocity of a Honda Civic over various time intervals, use the given position function, calculate displacements at the specific times, and divide by the respective time intervals.
Step-by-step explanation:
To calculate the average velocity of the Honda Civic for different time intervals, we use the position function x(t) = (alpha * t^2) - (beta * t^3) provided in the question, where alpha = 1.55 m/s² and beta = 4.70 x 10⁻² m/s³.
A. For the time interval from t=0 to t1=2.00 s, the average velocity is calculated as:
- First, we compute the car's displacement by plugging t1 into the position function: x(t1) = (1.55 m/s²)(2.00 s)² - (4.70 x 10⁻² m/s³)(2.00 s)³.
- Next, we divide the displacement by the time interval (t1 - 0) to find the average velocity.
B. Similarly, for the interval t=0 to t2=3.96 s, we calculate the displacement at t2 and divide by t2 to find the average velocity.
C. To find the average velocity for the interval from t1=2.00s to t2=3.96s, we calculate:
- The displacement at t2 as before.
- The displacement at t1 as before.
- Subtract the displacement at t1 from that at t2 to get the car's change in position for this interval.
- Divide this change in position by the time difference (t2 - t1) to determine the average velocity.