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`        The speed of a particle of mass m varies with the distance x as v(x) = ax -n. Assume v(x = O) = 0 at t = 0. (a) Find the force F(x) responsible. (b) Determine x(t) and`
one year ago

```							(a) Velocity of the particle, v = ax-n                         (dv/dx) = aAcceleration the particle = b = v(dv/dx)                                  b = (ax-n)(a)                                  b = a2x-anSo force, F(x) = m*b       F(x) = m(a2x-an) (b) Velocity of the particle = v = (dx/dt) = ax-n                                    [dx/(ax-n)] = dtIntegrating both sides, we get,                       {log[mod(ax-n)]}/a = t + c Put x=0 at t=0                                      (log n)/a = c                       {log[mod(ax-n)]}/a = t + (log n)/aSo,                                                 x(t) = (neat + n)/a
```
one year ago
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