Hey, I suspect that this is probably quite simple, but I'm a bit stuck on it, or the 2nd part at least. 1. The problem statement, all variables and given/known data 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. 3. 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.