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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?

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  • $\begingroup$ 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'. $\endgroup$ Jun 19, 2019 at 1:13

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The problem needs to tell you whether the penny is thrown upward or downward. This will let you decide whether the initial velocity is positive or negative.

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  • $\begingroup$ The problem said it was thrown from a tower, so I assume downward. $\endgroup$
    – user163862
    Sep 26, 2017 at 21:02
  • $\begingroup$ Looks like the problem may have been poorly-written. As you clearly understand, the penny can be thrown either up or down. We need this information to determine the sign of the velocity; I don't think it's reasonable to simply assume that the velocity must be negative. $\endgroup$
    – MMASRP63
    Sep 26, 2017 at 21:18
  • $\begingroup$ In defense of the problem, on the other hand, velocity is a vector (has magnitude and direction) while speed is a scalar (has only magnitude). Speed is the absolute value/magnitude/norm of velocity. Since the problems specified a velocity of 50 ft/s rather than a speed, we can assume that the specified velocity is positive rather than negative. But then, we run into another issue: how is the coordinate system defined? Traditionally, up is the positive direction and down is the negative direction, but there are reasons to reverse that. So I still think the problem is unclear. $\endgroup$
    – MMASRP63
    Sep 26, 2017 at 21:20
  • $\begingroup$ Yes, it was certainly confusing to me. $\endgroup$
    – user163862
    Sep 26, 2017 at 21:31
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I throw a ball straight up in the air. In the moment after I throw it, the velocity is positive - after all, it's I threw it upwards - but the acceleration is negative - gravity is pulling it down to Earth. Why doesn't the ball move downwards? Gravity has to 'exhaust' the balls velocity before the downward acceleration due to gravity actually moves the ball downwards.

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  • $\begingroup$ I see that. but since it was thrown from a tower, I assumed it was thrown down. $\endgroup$
    – user163862
    Sep 26, 2017 at 21:10

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