Problem 12-18: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Rocket Altitude via Kinematics and Integration

This lesson finds the time for a rocket to reach a given altitude when acceleration is a function of position. The method combines the kinematic identity a = v dv/ds with separation of variables, completing the square, and a standard logarithmic integral formula.

Question:
The acceleration of a rocket traveling upward is given by a equals 6 plus 0.02 s, in meters per second squared, where s is in meters. Determine the time needed for the rocket to reach an altitude of s equals 100 meters. Initially, v equals 0 and s equals 0 when t equals 0.

In this lesson, you will learn to:
• Apply the kinematic identity $a = v\,\frac{dv}{ds}$ to convert a position-dependent acceleration into a separable ODE
• Integrate to find velocity as a function of position and set up a time integral
• Simplify a radical integrand by completing the square
• Evalua