Thread: Quadratic word problem

The distance, d (in metres), which an object travels. is given by the equation where u is the initial velocity (in metres per second) and t is the time in seconds it has been travelling. Show that there is only one value for t when

I'm having real trouble solving this equation for t using any algebraic method that I've learnt for quadratic equations.
I can't figure out how to put it into the quadratic formula simply for the fact that i can't get any of the variables by themself on either side of the equation to set as x.

The steps I've tried so far in order to rearrange for t are:

add 8t^2 to both sides

divide both sides by t

take d/t away from both sides

and here is where i lose track, because i figure out that i can't rearrange for t at all. i've considered converting d/t into V (final velocity) but i can't see that helping much.
Any suggestions would be much appreciated.

Originally Posted by mattty

The distance, d (in metres), which an object travels. is given by the equation where u is the initial velocity (in metres per second) and t is the time in seconds it has been travelling. Show that there is only one value for t when

.

Rearrange the expression for :



This is an equation relating and .

If for some particular and we wish to solve for we will use the quadratic formula. Now the discriminant for the quadratic is:



and it is well known that we have no real roots for if , two real roots if , and exactly one real root if .

The last condition above is the one applicable here.

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Many thanks for this, apparently maths at 3am isn't my strong point