Can someone explain the confusion with these basic motion equations?

[FlamingAero]

I have been reviewing the basic two-dimensional motion equations and I've discovered a conundrum that is causing me much confusion. For example, here is a basic formula with variables:

$v^2 = vi^2 + 2ax$

$v = ?$

$vi = 27$

$a = -7.5$

$x = 49$

Therefore:

$v^2 = 27^2 + 2(-7.5)(49)$

$v^2 = 729 + -735$

$v = √(-6)$

When I input the square root of (-6) into my calculator (a TI-83+), I receive a ERR:NONREAL ANS message. Are these values not compatible with this formula?

Here's another similar example, this time with the formula:

$ΔX = vi*t + (1/2)at^2$

$ΔX = 49$

$vi = 27$

$a = -7.5$

$t = ?$

I have no idea how to even arrange the equation in terms of $t$. Is this formula limited to solving displacement?

Thank you for your help and guidance.

 

[Doc Al]

Are these values not compatible with this formula?

Your values are just physically impossible. Given that initial velocity and acceleration, you'll never achieve x = 49. (Figure out the maximum value of x.)

Similar issue with the other formula for time. (In general, you can surely solve for the time. You'll get a quadratic equation.)

 

[FlamingAero]

Your values are just physically impossible.

I now see my error. The value $ΔX = 49$ was rounded for significant figures, and should have instead been $ΔX = 48.6$

Thank you for your help.

 

[FaraDazed]

Yeah the second one is a quadratic so you can either set it to 0 and factorise to get your two answers or use the quadratic formula below

$$<br /> \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$