The velocity of a bug is moving along the y-axis is given by the equation: v(t)= (2t-1)(t-5)^2. At what time(s) on the interval [0, 10] does the bug change directions?

Answer 1

Direction changes whenever velocity goes from negative to positive or positive to negative... The sign (+ or -) is just the direction because velocity is a vector.

Therefore you need to find where the equation equals zero... use any root finding method or graph it or just simply set it equal to zero and solve. You get that velocity is zero at t = 0.5 and t = 5. So these are the two options. By plugging in zero (just a random time before t = 0.5) and then plugging in 1 (just another random time aster t = 0.5 to check if sign changes), you can see it goes from negative to positive so at t = .5 the bug changes directions. Do the same thing for t = 5, however and you'll see that it stays positive, so this just means it stopped and then went again but did not change direction.