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A particle is moving horizontally along the x-axis. Its position (in ft) is: s(t)=t^3-18t^2+33t+14 where t is in sec.
Find the time at which the particle switches from moving left to moving right.
t= ___ sec.

A particle is moving horizontally along the xaxis Its position in ft is stt318t233t14 where t is in sec Find the time at which the particle switches from moving class=

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kudzordzifrancis

Answer:

t=11 sec

Step-by-step explanation:

The position of the particle moving along the x-axis is given by:

[tex]s(t) = {t}^{3} - 18 {t}^{2} + 33t + 14[/tex]

The velocity is given by:

[tex]s'(t) = 3 {t}^{2} - 36{t} + 33[/tex]

If s'(t)>0 then the particle is moving right.

[tex]3 {t}^{2} - 36{t} + 33 \: > \: 0 \\ {t}^{2} - 12{t} + 11\: > \: 0[/tex]

[tex] \implies \: t \: < \: 1 \: or \: t \: > \: 11[/tex]

This means that the particle is moving left when

[tex]1 \: < \: t \: < \: 11[/tex]

The particle changes direction at time t=1 or t=11

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