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## Homework Statement

The displacement s of a particle moving in a straight line as a function of time t is given by s^3 = t. Find the value of n if at any time t:

constant * s^n

represents: (i) the speed of the particle; (ii) the force acting on the particle.

## The Attempt at a Solution

For (i), I tried to derive a differential equation by writing:

ds/dt = k*s^n (where k is constant)

=> ds = k*t^(n/3) dt

By integrating both sides:

s = [k/((n/3)+1)] t^((n/3)+1) + c

I then hypothesised that we wanted ((n/3)+1) to be 1/3, because s=t^(1/3).

Hence, n = -2 is my answer. Is it right, or am I off-track?

For part (ii), I don't know. I know we can write force = mass * acceleration, hence F = m*s'' (s differentiated twice) but that doesn't seem to give me an equation I can solve. I know acceleration can be written in other ways, so should I write it as dv/dt or possibly v*dv/ds?

Thanks.