If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
Practice Questions
1 question
Q1
If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
(2, 3, 4)
(4, 6, 8)
(2t, 3t, 4t)
(0, 0, 0)
Velocity vector = dr/dt = (2, 3, 4)
Questions & Step-by-step Solutions
1 item
Q
Q: If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
Solution: Velocity vector = dr/dt = (2, 3, 4)
Steps: 6
Step 1: Understand that the position vector r is given as r = (2t, 3t, 4t). This means the position of the point changes with time t.
Step 2: To find the velocity vector, we need to differentiate the position vector r with respect to time t. This means we will find the derivative of each component of r.
Step 3: Differentiate the first component 2t with respect to t. The derivative is 2.
Step 4: Differentiate the second component 3t with respect to t. The derivative is 3.
Step 5: Differentiate the third component 4t with respect to t. The derivative is 4.
Step 6: Combine the derivatives from Steps 3, 4, and 5 to form the velocity vector. The velocity vector is (2, 3, 4).
