Question

A bird is flying due east. Its distance from a tall building is given by x(t)=30.0m+(11.7m/s)t−(0.0450m/s3)t3. A) What is the instantaneous velocity of the bird when t = 8.00 s

Answer 1

We are given the expression for the distance 'x' in terms of 't'.

We need to first differentiate x(t) to find an expression for the velocity in terms of 't'

$x(t) = 30+11.7t-0.0450t^3$
$\frac{dx}{dt} = 11.7(1)t^{1-1}-(0.0450)(3)t^{3-1}$
$v= \frac{dx}{dt}=11.7-0.135t^2$

The value of v when t = 8

$v(8)=11.7-0.135(8)^2 = 3.06m/s$