A bird is flying due east. Its distance from a tall building is given by x (t) = 28.0 m + (12.4 m/s) t - (0.0450 m/s3) t3. What is the instantaneous velocity of the bird when t = 8.00s?

3.76 m/s

Explanation:

Instantaneous velocity: This can be defined as the velocity of an object in a non uniform motion. The S. I unit is m/s.

v' = dx (t) / dt ... Equation 1

Where v' = instantaneous velocity, x = distance, t = time.

Given the expression,

x (t) = 28.0 m + (12.4 m/s) t - (0.0450 m/s³) t³

x (t) = 28 + 12.4t - 0.0450t³

Differentiating x (t) with respect to t.

dx (t) / dt = 12.4 - 0.135t²

dx (t) / dt = 12.4 - 0.135t²

When t = 8.00 s.

dx (t) / dt = 12.4 - 0.135 (8) ²

dx (t) / dt = 12.4 - 8.64

dx (t) / dt = 3.76 m/s.

Therefore,

v' = 3.76 m/s.

Hence, the instantaneous velocity = 3.76 m/s