Total distance traveled by particle

BrownianMan

If s(t) = 2t^3 - 21t^2 + 60t is the position function of a particle moving in a straight line, would you be able to find its total distance traveled in, say 3 seconds, by finding s(0), s(1), s(2), s(3), and calculating the absolute value between each of them and then summing those values, as opposed to differentiating the function first, setting the derivative to 0, and solving for t?

Would you get the same answer?

sjb-2812

What do you hope to gain by setting ds/dt to 0?

BrownianMan

That's the standard way of solving such a problem - or at least how we've been taught. You differentiate to find the velocity, then set velocity to 0 to find the intervals when the particle is moving in a positive and in a negative direction.

sjb-2812

OK, just making sure you understand. What would happen in both cases if the function was say, s(t) = 4t²-4t+1?