An object is at x = 0 at t = 0 an moves along the x axis according to the veloci

Question

An object is at x = 0 at t = 0 an moves along the x axis according to the velocity-time graph shown below.

(a) At what time is the object farthest from x = 0? _______s

(b) What is the final position x of the object at t = 18 s? _______m

(c) Through what total distance has the object moved between t = 0 and t = 18 s? _______m

An object is at x = 0 at t = 0 an moves along the x axis according to the velocity-time graph shown below. (a) At what time is the object farthest from x = 0? _______s (b) What is the final position x of the object at t = 18 s? _______m (c) Through what total distance has the object moved between t = 0 and t = 18 s? _______m

Explanation / Answer

Part A)

The distance is the area under the curve. The greatest area total occurs at the time of 18 sec

Thus the farthest from zero is at 18 sec...

Part B)

We need to add all of the areas...

We have two rectangles and three triangles...

d = (-12)(4) + (.5)(-12)(2) + (.5)(18)(3) + (18)(4) + (.5)(18)(5)

d = 84 m

Part C)

Total Distance = (12)(4) + (.5)(12)(2) + (.5)(18)(3) + (18)(4) + (.5)(18)(5)

Distance = 204 m

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