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Chapter 1: Q8E (page 58)

A bird is flying due east. Its distance from a tall building is given by

xt=28.0m+12.4m/st-0.0450鈥�m/s3t3.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鈥�s isv8.00=3.76m/s

Step by step solution

01

Identification of the given data

The distance function for the bird is,

鈥�xt=28.0m+12.4m/s脳t-0.0450m/s3脳t3

and the given time ist=8.00s

02

Calculation of the instantaneous velocity of the bird

The instantaneous velocity can be expressed as,

vi=dsdt

Where viis the instantaneous velocity, is the displacement, and istime.

The expression for the distance is given as,

xt=28.0m+12.4鈥�m/st-0.0450m/s3t3

Instantaneous velocity expressed as

vi=ddt28.0鈥�m+12.4m/st-0.0450m/s3t3=12.4m/s-0.135m/s3脳t2

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

v8.00=12.4m/s-0.135鈥�m/s3脳8.00s2=3.76m

Thus, the instantaneous velocity is v8.00=3.76鈥�m/s

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