Word problem involving instantanous velocity and acceleration

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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
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c0der

Trying to learn programming, it's difficult but can be fun :)

Updated on February 26, 2020

Comments

  • c0der
    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?

  • c0der
    c0der over 8 years
    How could I find out how long it was in the air
  • EgoKilla
    EgoKilla over 8 years
    Hint: what's the height of the ball when it hits the ground?
  • c0der
    c0der over 8 years
    When it hit's the ground, wouldn't the height be 0?
  • EgoKilla
    EgoKilla over 8 years
    Indeed and you have a function that relates height and time.
  • c0der
    c0der over 8 years
    So i'm guessing I just plug in zeros for t then?
  • EgoKilla
    EgoKilla over 8 years
    Your 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.
  • c0der
    c0der over 8 years
    So 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?
  • EgoKilla
    EgoKilla over 8 years
    I 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 $t$.
  • c0der
    c0der over 8 years
  • dimaastronom
    dimaastronom over 8 years
    The 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.