[T] Let \(\mathbf{r}(t)=\left\langle t, 2 t^{2}, 4 t^{2}\right\rangle\) be the position vector of a particle at time t (in seconds), where \(t \in[0,10]\) (here the components of r are expressed in centimeters).

a. Find the instantaneous velocity, speed, and acceleration of the particle after the first two seconds. Round your answer to two decimal places.

b. Use a CAS to visualize the path of the particle defined by the points \(\left(t, 2 t^{2}, 4 t^{2}\right)\) , where \(t \in[0,60]\).

Text Transcription:

r(t) = langle t, 2t^2, 4t^2 rangle

t in [0,10]

(t, 2t^2, 4t^2)

t in [0,60]

FST10Midterm1PracticeQuestions(Lectures1-4) Lecture1:FoodanditsRepresentatives:AnIntroduction 1) Whichofthefollowingcontainsthecorrectchronologicalorderofevents A) Agricultural,Industrial,Hunter-Gatherer B) Industrial,Agricultural,Hunter-Gatherer C) Hunter-Gatherer,Industrial,Agricultural D) Agricultural,Hunter-Gatherer,Industrial E) Noneoftheabove 2) WhichofthefollowingexplainswhyNeanderthalswereforagersand scavengers A) Theydidnotknowhowtocook B) Theywerenomads C) Nofoodstorage D) AandB E) BandC 3) Whichofthefollowingresultedfromcavemencookingfood A) Smallerteeth B) Increasedenergy C) Smallergut D) AandBonly E) Alloftheabove 4) Whichofthefollowingisadisadvantageofsettlersonnewland A) Ruinedsoil B) Smallamountsoffood C) Bettercrops D) Newcultivationskills E) AandB 5) Trueorfalse:Kosherfoodisunblessed. 6) Whichofthefollowinghavebeenassociatedwithincreasesinhumanbrainsize A)Harnessingfire B) Theweather C) Increasedmeatconsumption D) AandC E) Noneoftheabove 7) Whichofthefollowinghavebeenassociatedwithincreasesinhumanbrainsize A)Harnessingfire B)Theweather C)Increasedmeatconsumption D)AandC E)Noneoftheabove 8) Whichofthefollowingareconsideredphysiologicalaspectsoffood A)Energy B)Metabolism C)Noneoftheabove D)Nutrition E)A,B,andD 9) T/F:Wat