bc calcus chapter 12

For t≥0, a particle moving in the xy-plane has velocity v(t) = <5e^-t, sin(1+t)>. What's the total distance the particle traveled from 0 ≤ t ≤ 2?

• 1.861 meters

• 2.236 meters

• 1.695 meters

• 4.613 meters

A moving particle has position (x(t), y(t)) at time t. The particle's position at time t = 1 is (2, 6) and the velocity vector at any time t>0 is given by (1-1/t², 2+1/t²). Find the position of the particle at time t = 6.

• (25/6, 65/6)

• (101/6, 37/6)

• (65/6, 25/6)

• (37/6, 101/6)

An object moves in the xy-plane so that its position at any time t is given by the parametric equations x(t) = t³ – 3t² + 2 and y(t) = √(t² + 16). What is the rate of change of y with respect to x when t = 3?

• 1/90

• 1/15

• 3/5

• 5/2

Snow is falling at a rate of r(t) = 2e^–0.1t inches per hour, where t is the time in hours since the beginning of the snowfall. Which of the following expressions gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours?

• 2e^–0.5 – 2

• 0.2 – 0.2e^–0.5

• 4 – 4e^–0.5

• 20 – 20e^–0.5

An object moves along a straight line so that at any time t its acceleration is given by a(t) = 6t. At time t = 0, the object's velocity is 10 and the object's position is 7. What is the object's position at time t = 2?

• 22

• 27

• 28

• 35

For x(t) = 3t²-3, y(t) = 2t +1, find the slope of the tangent at t = 1

• 1/3

• 1

• 2

• 3

Tags

CCSS.HSF.TF.B.7

In the xy-plane, a particle is moving so that when t >0, its x-coordinate is t³-t and its y-coordinate is (2t-1)³. What is the acceleration vector when t = 3?

• (24, 125)

• (26,125)

• (18,120)

• (28,120)

The position of a particle moving in the xy-plane is given by r(t) = (ln(t²+2t), 2t²) when time t>0. What is the particle's velocity vector at t =2?

• (3/4, 8)

• (3/4, 4)

• (1/8, 8)

• (1/8, 4)

(No Calc) At time t ≥ 0, a particle moving in the xy-plane has velocity vector given by v(t) = 〈 t², 5t〉. What is the acceleration vector of the particle at time t = 3?

• 〈 9, 45/2〉

• 〈6, 5〉

• 〈2, 0〉

• √306

• √61

Find an equation for the instantaneous velocity v(t) if the path of an object is defined as s(t) for any point in time t.

and then replace t = 1

• 34

• 17

• 2

• 9