The locationP(t)of an object moving in thexy-plane at timetseconds is given by the equationsP(t)=(x(t),y(t)), wherex(t)=a +5tandy(t)=b +9t,a,bare constants and distances are measured in units of meters. The equationsx(t), y(t)describelinear parametrized motion; see section 10.1 of the textbook for review.(a) The location of the object at timet=1is (

a+5

b+9

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

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

m/s; this is called the instantaneous horizontal velocity at timet=1. (d) What is the instantaneous horizontal velocity of the object at timet?

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

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

m/s; this is called the instantaneous vertical velocity at timet=1. (g) What is the instantaneous vertical velocity of the object at timet? (h) The line along which the object is moving in the plane has the equation:y=

. (i) Letd(t)be the distance the object has traveled aftertseconds. The formula ford(t)is (j) The instantaneous rate of change ofd(t)at timetis

. This is called thespeedalong the line of motion