Question

Find the unit tangent vector to the curve at the point with the given value of the parameter t.

Answer 1

To find the unit tangent vector to the curve at the given point, follow these steps: Find the tangent line at t = 25 s, determine the endpoints of the tangent, and solve for the slope.

Step-by-step explanation:

To find the unit tangent vector to the curve at the point with the given value of the parameter t, follow these steps:

1. Find the tangent line to the curve at t = 25 s.
2. Determine the endpoints of the tangent. These correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s.
3. Plug these endpoints into the equation to solve for the slope, v.