BC Calc Vector Calculus Practice

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)

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

For x(t) = 3t²-3, y(t) = 2t +1, find the speed of the particle at t =1.

• 0.333

• 2.828

• 6.164

• 6.325

Find the speed of the particle at t = 3 for the parametric equation For x(t) = 3t³-1 and y(t) = t-1

• 1/27

• 9.001

• 1/9

• 81.006

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)