# Confusion on when velocity and acceleration are positive vs negative

This is given in a calculus math class not physics. The question is the typical one of how long does it take a penny to hit the ground when thrown from a 300 ft tower with initial velocity of 50 ft/sec. We have learned derivatives but not integration. So, I will use the equation: $s(t)=s_0 + v_0t -1/2 at^2$.

I use $300$ for the distance. Here is my question(s): I can see that since the object / penny is falling downwards that the acceleration is $-32 ft/s^2$. Wouldn't that also mean that the initial velocity should be negative, $-50$?.

With acceleration negative and velocity positive, I get $16t^2+50t-300=0$ which gives the correct answer of 3.04 seconds.

But if I use also a negative initial velocity of $-50$, then I get $16t^2-50t-300=0$ which of course does not give the correct answer.

If the acceleration is negative, why isn't the initial velocity also negative?

• Do not forget both velocity and acceleration could have different signs. Negative acceleration does not always mean deceleration, directions come into play. The question seems not clear on 'direction'. Jun 19, 2019 at 1:13