A rabbit runs across a parking lot on which a set of coordinates axes has been d
ID: 1599392 • Letter: A
Question
A rabbit runs across a parking lot on which a set of coordinates axes has been drawn. The coordinates(meters) of the rabbit's position as functions of time t(seconds) are given by:
x = -0.31t2 + 7.2t + 28 y = 0.22t2 - 9.1t + 30
Given the information above, answer parts a, b, c, d, and e below. Show all work and give explanation. Be sure to properly use vector notation where needed.
a) Obtain the speed of the rabbit as a function of time.
b) When does the rabbit run slowest?
c) Where is the location of the rabbit when it is running slowest?
d) What is the rabbit's velocity when the rabbit runs slowest?
e) In which direction is the rabbit running at its slowest velocity, in terms of an angle with respect to the positive x direction?
Explanation / Answer
v(t) = ds(t)/dt
vx(t) = dx(t)/dt = -0.6*t + 7.2
vx(15) = -0.6*15 + 7.2 = -1.8
vy(t) = dy(t)/dt = 0.44*t - 9.1
vy(15) = 0.44*15 - 9.1 = -2.5
||v|| = sqrt(vx^2 + vy^2) = 3.08 (I assume it is m/s)
a(t) = dv(t)/dt
ax(t) = dvx(t)/dt = -0.6
ay(t) = dvy(t)/dt = 0.44
Since the acceleration is constant in both directions, you don't have to worry about time.
||a|| = sqrt(ax^2 + ay^2) = 0.744 (I assume m/s^2)