Physics work again NOT in the book!!!!?

Question

A person looking out the window of a tall office building observes what he suspects is a UFO. The person records the position of the object as a function of time and finds it is given by *r*(t) = -(5.0 m/s)t*i*+ (10.0 m/s)t*j*+ [(7.0 m/s)t - (3.0 m/s2)t2]*k*

(a) Find the displacement, velocity, and acceleration vectors for the object at t = 2.0 s.
r(2s)= ____i +____ j +_____k
v(2s)=____i +____ j +_____k
a(2s)=____i +____ j +_____k

b) Is there a time when the object has a velocity of zero?


c) Is the acceleration of the object constant, or does it change with time?

Answer 1

a. r(2s) just substitute in t=2 and calculate. I am assuming that t2 means t^2.

R = -10i +20j + (14 - 12)k
R = -10i + 20j + 2k meters

For velocity, take the derivative
d(-5t)/dt = -5
d(10t)dt = 10
d(7t - 3t^2)/dt = 7 - 6t
So the velocity is:
V = -5i + 10j + (7 - 6t)k meters/second
At t = 2, again just substitute this value in for t:
V = -5i + 10j - 5k meters/second

The acceleration is the derivative of the velocity and it is only the k term that is non zero since the i and j terms are both constance. So:
A = d(7 - 6t)dt = -6k meters/second^2

b. The object never has zero velocity since the i and j components are constant.

c. The acceleration is constant at 6 m/s and only in the k direction.