Final answer:
The average velocity of the object over the time interval [2,4] is calculated by dividing the change in position by the change in time, resulting in an average velocity of 20 m/s.
Step-by-step explanation:
Average velocity is defined as the total displacement of an object divided by the total time taken to cover that displacement. It provides a measure of how fast and in what direction an object is moving, taking into account both the distance traveled and the time it took to cover that distance.
The average velocity of an object over a specified time interval is calculated by determining the total displacement of the object during that time interval and then dividing it by the total time taken.
Determine the Change in Position (Displacement):
Find the initial position and the final position of the object.
Calculate the change in position (ΔxΔx) by subtracting the initial position from the final position.
Determine the Change in Time:
Find the initial time and the final time during which the motion occurs.
Calculate the change in time (ΔtΔt) by subtracting the initial time from the final time.
The question asks to find the average velocity of an object over a specified time interval. To calculate this, we need to use the formula for average velocity, which is the change in position (Δs) divided by the change in time (Δt).
Using the provided position values, s(2) = 137 and s(4) = 177, we can find the change in position:
- Δs = s(4) - s(2) = 177 - 137 = 40
Next, we find the change in time:
Now we can calculate the average velocity:
- Average velocity = Δs / Δt = 40 / 2 = 20 m/s
The average velocity of the object over the interval from time t = 2 to time t = 4 is 20 m/s.