The location P(t) of an object moving in the xy-plane at time t seconds is given by the equations P(t)=(x(t),y(t)), where x(t)=a +8t and y(t)=b +6t, a, b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review.

(a) The location of the object at time t=1 is (

,

)
(b) The average rate of change of x(t) between 1 and 2 seconds is

m/s; this is called the average velocity of x(t) on the time interval [1,2].
(c) The instantaneous rate of change of x(t) at time t=1 is

m/s; this is called the instantaneous horizontal velocity at time t=1.

(d) What is the instantaneous horizontal velocity of the object at time t?

(e) The average rate of change of y(t) between 1 and 2 seconds is

m/s; this is called the average velocity of y(t) on the time interval [1,2].
(f) The instantaneous rate of change of y(t) at time t=1 is

m/s; this is called the instantaneous vertical velocity at time t=1.
(g) What is the instantaneous vertical velocity of the object at time t?

(h) The line along which the object is moving in the plane has the equation: y=

x+

.
(i) Let d(t) be the distance the object has traveled after t seconds. The formula for d(t) is

.
(j) The instantaneous rate of change of d(t) at time t is

. This is called the speed along the line of motion.