Question

The position of an object moving along a straight line for

t 0 is given by s1(t) =t3 +2, and the

position of a second object moving alongthe smae line is given by

s2(t) = t2. If bothobjects begin at t = 0, at

what time is the distance between theobjects a minimum?

Answer 1

Answer:

at 2/3 seconds

Step-by-step explanation:

S1(t) = t³ + 2

Average speed, dS1/dt = 3t²

S2(t) = t²

Average speed, dS2/dt = 2t

The distance between the objects is

dS1/dt - dS2/dt

= 3t² - 2t

The time the distance between the two object is at minimum is when the distance is 0

That is, when

3t² - 2t = 0

t(3t - 2) = 0

t = 0 or 3t - 2 = 0

t = 0 or t = 2/3