Suppose the velocity of a body moving along the s-axis is ds/dt = 9.8t - 8. Is i

Question

Suppose the velocity of a body moving along the s-axis is ds/dt = 9.8t - 8. Is it necessary to know the initial position of the body to find the body's displacement over some time interval? Justify your answer. A) No, the initial position is necessary to find the curve s = f(t) but not necessary to find the displacement. The A) initial position determines the integration constant. When finding the displacement the integration constant is subtracted out. B) No, displacement has nothing to do with the position of the body. C) Yes, integration is not possible without knowing the initial position. D) Yes, knowing the initial position is the only way to find the exact positions at the beginning and end of the time interval. Those positions are needed to find the displacement.

Explanation / Answer

Option A is correct because we can use definite integration to find the displacement for any interval of time. Initial position is not needed.

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