Question

suppose a particle moves along a straight line. the position at time t is given by ( s(t)=7t - 2t^{2},tgeq0 ), where t is measured in seconds and ( s(t) ) is measured in meters. complete parts (a) - (d) below. at ( t = 0 ), the particle is at ( s(0)= ) (type an integer or a fraction.) (ii) is there another time at which the particle visits the location where it was at time 0? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the particle revisits the location where it was at time 0 at ( t = ). b. the particle never revisits the location where it was at time 0.

Explanation:

Step1: Find \(s(0)\)

Substitute \(t = 0\) into \(s(t)=7t - 2t^{2}\).

$$s(0)=7\times0-2\times0^{2}=0$$

Step2: Find if there is another \(t\) such that \(s(t)=0\)

Set \(s(t)=0\), so \(7t - 2t^{2}=0\). Factor out \(t\): \(t(7 - 2t)=0\).
Using the zero - product property \(t = 0\) or \(7-2t=0\).
Solve \(7 - 2t=0\) for \(t\):

$$
LATEXBLOCK0
$$

Answer:

(i) \(0\)
(ii) A. The particle revisits the location where it was at time \(0\) at \(t = 3.5\)