The acceleration of a particle which is moving along a straight line is given by a = –kv0.5, where a is in meters per second squared, k is a constant, and v is the velocity in meters per second. determine the velocity as a function of both time t and position s. evaluate your expressions for t = 2.7 sec and at s = 6 m, if k = 0.3 m0.5 sec–1.5 and the initial conditions at time t = 0 are s0 = 2.6 m and v0 = 2.7 m/sec.

For t=2.7s and k=0.3 m/s:

For s=6m and k=0.3 m/s:

Explanation:

Definition of acceleration:

we integrate in order to find v(t):

       A=constant

Definition of velocity:

We integrate:

      B=constant

But:

⇒

         D=other constant

Initial conditions:t = 0 are s0 = 2.6 m and v0 = 2.7 m/sec:

So:

For t=2.7s and k=0.3 m/s:

For s=6m and k=0.3 m/s:

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