Question

Some rental cars have a GPS unit installed, which allows the rental car company to check where you are at all times and thus also know your speed at any time. One of these rental cars is driven by an employee in the company's lot and, during the time interval from 0 to 10 s, is found to have a position vector as a function of time of
rarrow(t) =
(24.4 m) − t(12.3 m/s) + t2(2.43 m/s2), (74.4 m) + t2(1.80 m/s2) − t3(0.130 m/s3)
.
(a) What is the distance of this car from the origin of the coordinate system at t = 5.89 s?
1

(b) What is the velocity vector as a function of time?
varrowitalic(t) = m/s

(c) What is the speed at t = 5.89 s?