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?

Question

Mathematics

Gage Washington

31 May, 02:04

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?

+2

Answers (1)

Know the Answer?

Kian Tucker · Answer 1

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

The position of an object moving along a straight line fort 0 is given by s1 (t) = t3 + 2, and theposition of a second object moving alongthe smae line is given bys2 (t) = t2. If bothobjects begin at t = 0, atwhat time is the distance between theobjects a minimum?

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?