Physical Interpretation for two answers for time

[mateomy]

When you solve the motion equation

$$x=x_0 +v_0t +\frac{1}{2}at^2$$

you get two answers for t. One being a negative due to the quadratic. What is the physical interpretation of this? Its driving me nuts.

 

[tiny-tim]

hi mateomy!

you get two answers for t. One being a negative due to the quadratic. What is the physical interpretation of this? Its driving me nuts.

that's the standard constant acceleration equation for a particle going vertically up at speed v₀ and height x₀ at time t …

the two values of t for x = 0 are the time in the future when it will hit the ground, and the time in the past when it would have left the ground if it had been thrown from there (or below)

 

[mateomy]

Go'bless you, Toiny Tim (Harsh cockney accent). What if, say...it left from the ground?

 

[tiny-tim]

wotcher, me ol' mateomy!

Go'bless you, Toiny Tim (Harsh cockney accent). What if, say...it left from the ground?

from the foot of the apples an' pears?

then the negative answer would be the time before it reaches height x₀ …

'nuff said? ​

 

[mateomy]

Got it down solid now. Thanks for the clarification.