Answer :

Edufirst

Answer:

  • The procedure is: solve the quadratic equation for [tex]t[/tex].

Explanation:

This question assumes uniformly accelerated motion, for which the distance d a particle travels in time t is given by the general equation:

  • [tex]d(t)=d_0+v_0t+at^2/2[/tex]

That is a quadratic equation, where the independent variable is the time [tex]t[/tex].

Thus, the procedure that will find the time t at which the distance value is known to be D is to solve the quadratic equation for [tex]t[/tex].

To solve it you start by changing the equation to the general form of the quadratic equations, rearranging the terms:

  • [tex](a/2)t^2+v_0t+(d_0-D)=0[/tex]

Some times that equation may be solved by factoring, and always it can be solved by using the quadratic formula:

  • [tex]t=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Where:

[tex]a=-a/2\\ \\ b=v_0\\ \\ c=d_0-D[/tex]

That may have two solutions. Some times one of the solution makes no physical sense (for example time cannot be negative) but others the two solutions are valid.

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