8. [9/12 Points] DETAILS PREVIOUS ANSWERS MY NOTES 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 +5t and y(t)=b +10t, a,b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrization; see section 10.1 of the textbook for review. (a) The location of the object at time t=1 is (|a + 5 b + 10 (b) The average rate of change of x(t) between 1 and 2 seconds is 5 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 5 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? 5 (e) The average rate of change of y(t) between 1 and 2 seconds is |10 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 |10 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? 10 (h) The line along which the object is moving in the plane has the equation: y= 2 x+ b X (i) Let d(t) be the distance the object has traveled after t seconds. The formula for d(t) is V ( x ( 1 ) ) 2 + ( x ( 1 ) ) 2 X (j) The instantaneous rate of change of d(t) at time t is This is called the speed along the line of motion