Calculus 3 question

Question

The velocity function for a moving object is 𝐯(𝑡) = <−2𝑡+9, (7−𝑡)^3/2, 1/3 t^2 - t >, where distances are in centimeters and time is in seconds. Find the following:

a). The function’s domain:

b). The speed (to the nearest 0.1 cm/sec) and direction of motion (round all final values to the nearest 0.1) at t = 3.

Answer 1

v(3) = <3, 8, 0> cm/sec = speed

3 cm/sec in the positive x axis

8 cm/sec in the positive y axis

0 cm/sec in the z axis

speed = sqr(3^2+8^2) = sqr73 cm/sec= about 8.544

= 8.5 cm/sec

in the positive xy plane direction at an angle = arctan(8/3= about 69.444 degrees= 69.4 degrees