Chapter 1: Q8E (page 58)

A bird is flying due east. Its distance from a tall building is given by
$x (t) = 28.0 m + (12.4 m / s) t - (0.0450 m / s^{3}) t^{3}$ .What is the instantaneous velocity of the bird when t = 8.00 s?

Short Answer

Expert verified

The Instantaneous velocity of the bird at $t = 8.00 s$ is $v_{8.00} = 3.76 m / s$

Step by step solution

Identification of the given data

The distance function for the bird is,

$x (t) = 28.0 m + (12.4 m / s) \times t - (0.0450 m / s^{3}) \times t^{3}$

and the given time is $t = 8.00 s$

Calculation of the instantaneous velocity of the bird

The instantaneous velocity can be expressed as,

$v_{i} = \frac{d s}{d t}$

Where $v_{i}$ is the instantaneous velocity, is the displacement, and istime.

The expression for the distance is given as,

$x (t) = 28.0 m + (12.4 m / s) t - (0.0450 m / s^{3}) t^{3}$

Instantaneous velocity expressed as

$v_{i} = \frac{d}{d t} (28.0 m + (12.4 m / s) t - (0.0450 m / s^{3}) t^{3}) = 12.4 m / s - (0.135 m / s^{3}) \times t^{2}$

Now,the substitution of $t = 8.00 s$ in above expression will result in,

$\begin{array}{rcl} v_{8.00} & = & 12.4 m / s - (0.135 m / s^{3}) \times {(8.00 s)}^{2} \\ = & 3.76 m \end{array}$

Thus, the instantaneous velocity is $v_{8.00} = 3.76 m / s$

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A bird is flying due east. Its distance from a tall building is given by
$x (t) = 28.0 m + (12.4 m / s) t - (0.0450 m / s^{3}) t^{3}$ .What is the instantaneous velocity of the bird when t = 8.00 s?

Short Answer

Step by step solution

Identification of the given data

Calculation of the instantaneous velocity of the bird

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A bird is flying due east. Its distance from a tall building is given byxt=28.0m+12.4m/st-0.0450 m/s3t3.What is the instantaneous velocity of the bird when t = 8.00 s?

Short Answer

Step by step solution

Identification of the given data

Calculation of the instantaneous velocity of the bird

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Fields in Physics

Measurements

Conservation of Energy and Momentum

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Energy Physics

Study anywhere. Anytime. Across all devices.

A bird is flying due east. Its distance from a tall building is given by
$x (t) = 28.0 m + (12.4 m / s) t - (0.0450 m / s^{3}) t^{3}$ .What is the instantaneous velocity of the bird when t = 8.00 s?