Question

A bird is flying due east. Its distance from a tall building is given by x(t)=29.0m+(11.0m/s)t−(0.0430m/s3)t3 . What is the instantaneous velocity of the bird when t = 8.00s?

Answer 1

To find the bird's instantaneous velocity at t = 8.00 s, differentiate the given position function and substitute t = 8.00 s into the resulting velocity function.

Step-by-step explanation:

The student's question is about calculating the instantaneous velocity of a bird at a given time using a provided position-time equation. To find the velocity at time t = 8.00 s, we need to differentiate the position function x(t) = 29.0 m + (11.0 m/s)t - (0.0430 m/s3)t3 with respect to time. This will give us the velocity function v(t), after which we can substitute the value of t to find the bird's instantaneous velocity.

The derivative of the position function is v(t) = dx(t)/dt = 11.0 m/s - 3(0.0430 m/s3)t2, which simplifies to v(t) = 11.0 m/s - 0.129 m/s3 t2. Substituting t = 8.00 s into the velocity function yields v(8.00) = 11.0 m/s - 0.129 m/s3 (8.00)2. After performing the calculation, we'll get the instantaneous velocity of the bird.