an object moves from the position (1,3,-5) to the position (-1,4,8) during time 8 s. what is the average speed?
To find the average speed of an object, you need to calculate the total distance traveled by the object and divide it by the total time taken.
The distance between two points in 3D space can be found using the formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]
Given the initial position (1, 3, -5) and the final position (-1, 4, 8), let's calculate the distance.
Distance = √[(-1 - 1)^2 + (4 - 3)^2 + (8 - (-5))^2]
= √[(-2)^2 + (1)^2 + (13)^2]
= √[4 + 1 + 169]
= √174
≈ 13.152946437965905
Now, divide the distance by the time taken to find the average speed.
Average Speed = Distance / Time
= 13.152946437965905 / 8
≈ 1.644118304745738
Therefore, the average speed of the object is approximately 1.644 m/s.