Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0000 362392 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0452 1213192 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0452 1213192 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1136 4199912 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1148 4227448 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1155 4245160 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1157 4275680 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1166 4298400 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1167 4298400 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1701 4975968 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1743 5168120 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1749 5189048 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1870 5400944 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1871 5401200 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

The Rocket Driven Car

As a car moves, it burns fuel to overcome resistance and drive the car forward. We can apply Newton's second law of motion to find the equation of motion of the car.

If the rocket engine burns up fuel at a constant ratekg/s, expelling the burnt product at a speedm/s relative to the car, and if the engine is turned on atthen atthe mass of the car iswhereis the initial mass of the car.

The rate of change of momentum of the expelled gases isand according to Newton's third law of motion this will result in an equal reaction force on the car.

If we assume that the total resistance to motion is proportional to the velocityof the car, then applying Newton's second law gives

Sincewe can write

Separating variables givesIfwhenthen

Exponentiation givesand further rearrangement and simplification gives