Word problem involving instantanous velocity and acceleration
1,878
Yes, $v(t) = -9.8t + 25$ and $a(t) = -9.8$.
Then $v(2) = 5.4$ and $a(2) = -9.8$.
To solve for when the ball hits the ground we simply set $f(t) = 0$ and solve for $t$.
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c0der
Trying to learn programming, it's difficult but can be fun :)
Updated on February 26, 2020Comments
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c0der over 3 years
I'll try to explain this clear enough:
Let's say a baseball is "popped up" into the air, and it's height (meters) after t minutes is represented by the function $f(t) = -4.9t^2+25t+3$.
I have to find the instantaneous velocity and the acceleration of $t$ when $t = 2$.
Would I be able to use the power rule to get the derivative of this function, and then plug in 2 to find the instantaneous velocity? Then would I be able to find the second derivative to find the acceleration?
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c0der over 8 yearsHow could I find out how long it was in the air
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EgoKilla over 8 yearsHint: what's the height of the ball when it hits the ground?
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c0der over 8 yearsWhen it hit's the ground, wouldn't the height be 0?
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EgoKilla over 8 yearsIndeed and you have a function that relates height and time.
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c0der over 8 yearsSo i'm guessing I just plug in zeros for t then?
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EgoKilla over 8 yearsYour function gives you height as a function of time, if you plugged in zeroes for $t$ then your function would return the height of the ball at time zero. That is not what you want.
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c0der over 8 yearsSo I would plug in the time when the ball hits the ground, and since the height is a function of time, this would give me the answer?
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EgoKilla over 8 yearsI don't think you're understanding what I mean the height is a function of time. Your function $f$ takes input $t$ t is a time, it outputs the height. You're trying to solve for $t$ the time when the ball hits the ground. You know the height is zero. Does this make more sense? You won't be plugging anything into $t$, you're trying to solve for $t$.
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c0der over 8 yearsLet us continue this discussion in chat.
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dimaastronom over 8 yearsThe function $f(t)=−4.9t^2+25t+3$ is way of finding height knowing $t$, but here is vice versa you know that height is zero or $f(t)=0$. So you just need to solve the equation you get from this.