Question

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 +6t and y(t)=b +7t, 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

Answer 1

Answer:

Vx = 6 m / s  and .vy = 7 m / s

Explanation:

a) Let's substitute the value of time in the equations

    x (1) = a +6

    y (1) = b + 7

b) and e) We calculate the position for t = 2 s

     x (2) = a +12

     y (2) = b +14

We calculate the average speed

      v = (x (2) -x (1)) / t2- t1

      vₓ = ((a + 12) - (a-6)) / (2-1)

      vₓ = 6 m / s

      $v_{y}$ = ((b + 14) - (b-7)) / 1

     $v_{y}$ = 7 m / s

c) and f) The instantaneous bone change calculates with the derivative

    vₓ = dx / dt

   vₓ = 6 m / s

That is constant for all time

   $v_{y}$ = dy / dt

    $v_{y}$ = 7 m / s

d) The speed on the x-axis is constant and is worth vx = 6 m / s