A particle P moves in a straight line so that at t seconds, its displacement, s meters from the starting point is s = t^3 - 7t^2 + 17t.

Question

A particle P moves in a straight line so that at t seconds, its displacement, s meters from the starting point is s = t^3 - 7t^2 + 17t. Determine the interval of the time when the particle is moving at an increasing speed.

Answer 1

For rectilinear motion, ie motion in one dimension that can either be in a positive or negative direction, one important concept is that speed is increasing whenever the signs of velocity and acceleration match.

So v(t) = s^'(t) = 3t² - 14t + 17 the discriminant of this quadratic is < 0 so it has no real zeros and is always +.

a(t) = v^'(t) = 6t - 14. which is negative for t < 7/3 and positive elsewhere.

Speed is increasing for t > 7/3 secs