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balu736 [363]
3 years ago
7

Supposing d(t) is known to have value D,

Physics
1 answer:
creativ13 [48]3 years ago
5 0

Answer:

  • The procedure is: solve the quadratic equation for t.

Explanation:

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

  • d(t)=d_0+v_0t+at^2/2

That is a quadratic equation, where the independent variable is the time t.

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 t.

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

  • (a/2)t^2+v_0t+(d_0-D)=0

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

  • t=\frac{-b+/-\sqrt{b^2-4ac} }{2a}

Where:

a=-a/2\\ \\ b=v_0\\ \\ c=d_0-D

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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