Question

Speed of a rocket At t sec after liftof, the height of a rocket is 3t 2 ft. How fast is the rocket climbing 10 sec after liftof?

Answer 1

Physically the derivative of the position of an object is equivalent to the function that describes its velocity. Therefore we will derive the function and then evaluate it within 10 seconds.

Our function is initially given as

$f(x) = 3t^2$

$f'(x) = 6t$

Evaluating at 10 seconds we have,

$f'(x) = 6(10)$

$f'(x) = 60$

Therefore the rocket climb to 60m/s