Question

A bird is flying due east. Its distance from a tall building is given by x(t)=25.0m+(11.7m/s)t-(0.400m/s³)t³. What is the instantaneous velocity of the bird when t=8.00s?

Answer 1

The instantaneous velocity of the bird when t=8.00s is approximately -4903.5 m²/s².

Step-by-step explanation:

To find the instantaneous velocity of the bird at a specific time, we need to find the derivative of the given equation for distance.

The equation for distance is x(t) = 25.0m + (11.7m/s)t - (0.400m/s³)t³.

Taking the derivative of x(t) with respect to t will give us the equation for velocity.

v(t) = 11.7m/s - 1.2m/s²t²

Substituting t = 8.00s into the equation, we can calculate the instantaneous velocity of the bird.

v(8.00s) = 11.7m/s - 1.2m/s²(8.00s)²

Using the equation, we can calculate:

v(8.00s) = 11.7m/s - 1.2m/s²(64.00s²) = 11.7m/s - 1.2m/s²(4096s²)

Calculating the expression inside the brackets, we get:

v(8.00s) = 11.7m/s - 1.2m/s²(4096s²) = 11.7m/s - 4915.2m²/s²

Simplifying, we find:

v(8.00s) ≈ -4903.5m²/s²

The instantaneous velocity of the bird when t = 8.00s is approximately -4903.5 m²/s².