Questions from Calculus

Q: Find the velocity, speed, and acceleration of a particle moving

Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (2t2 – 3) i + 2t j. Sketch the path of the particle and draw the position, velocity, and acceleration vect...

Q: A particle starts at the origin with initial velocity i - j

A particle starts at the origin with initial velocity i - j + 3k. Its acceleration is a(t) = 6t i + 12t2 j - 6t k. Find its position function.

Q: Find the tangential and normal components of the acceleration vector of a

Find the tangential and normal components of the acceleration vector of a particle with position function r(t) = t i + 2t j + t2 k

Q: Use Simpson’s Rule with n = 6 to estimate the length of

Use Simpson’s Rule with n = 6 to estimate the length of the arc of the curve with equations x = t2, y = t3, z = t4, 0 < t < 3.

Q: The helix r1(t) = cos t i + sin

The helix r1(t) = cos t i + sin t j + t k intersects the curve r2(t) = s1 + td i + t2 j + t3 k at the point (1, 0, 0). Find the angle of intersection of these curves.

Q: The figure shows the path of a particle that moves with position

The figure shows the path of a particle that moves with position vector r(t) at time t. (a). Draw a vector that represents the average velocity of the particle over the time interval 2 (b). Draw a v...

Q: Find and sketch the domain of the function. f (

Find and sketch the domain of the function. f (x, y) = sin-1(x + y)

Q: Find the curvature of the curve with parametric equations /

Find the curvature of the curve with parametric equations

Q: The curve with vector equation r(t) − t3 i

The curve with vector equation r(t) − t3 i + 2t3 j + 3t3 k is a line.

Q: If k(t) = 0 for all t, the

If k(t) = 0 for all t, the curve is a straight line.