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Physics Part I

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Two cars A and B are travelling in same direction with speed straight v subscript 1 space and space straight v subscript 2 respectively left parenthesis straight v subscript 1 greater than straight v subscript 2 right parenthesis. When car A is d distance behind the car B, the brakes on A are applied, causing retardation <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre>  Show that to prevent a collision between A and B it is necessary that
                        left parenthesis straight v subscript 1 minus straight v subscript 2 right parenthesis squared less than left parenthesis 2 αd right parenthesis


Here, inorder to prevent the collision of car A with B, the relative velocity of car A w.r.t. B should reduce to zero before car A undergoes the relative displacement of d w.r.t. car B.

Initial velocity of car A = straight v subscript 1

Initial velocity of car B = straight v subscript 2

Therefore,

Initial relative velocity of car A w.r.t. B is,

                   straight v equals straight v subscript 1 minus straight v subscript 2

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#6 {main}</pre>

Acceleration of car B = 0

Acceleration of car A w.r.t. car B = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre>

The relative displacement of car A w.r.t car B, when the relative velocity of car A w.r.t. B decreases to zero is given by,

            straight S equals fraction numerator 0 squared minus straight v squared over denominator negative 2 straight alpha end fraction equals fraction numerator straight v squared over denominator 2 straight alpha end fraction equals fraction numerator left parenthesis straight v subscript 1 minus straight v subscript 2 right parenthesis squared over denominator 2 straight alpha end fraction

For collision to avert S should be less than d.

i.e.                        S < d

rightwards double arrow                 fraction numerator left parenthesis straight v subscript 1 minus straight v subscript 2 right parenthesis squared over denominator 2 straight alpha end fraction less than straight d

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#6 {main}</pre>
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