My Math Forum Calculating the Acceleration

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January 25th, 2017, 11:07 AM   #1
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Calculating the Acceleration

So I'm stuck on another homework problem.

Quote:
 It took 5 s to come to a halt for a car to travel 200 m. Find its initial velocity and acceleration.
There is no equation this time to help me out and I'm unsure if I'm able to write this as function of time at this moment. Could I get another hint?

 January 25th, 2017, 11:32 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 you can always write $s(t) = \dfrac {a t^2}{2} + v_0 t + s_0$ $v(t) = a t + v_0$ so if you are given a time $T$ and distance $D$ you can write $s_0=0,~s(T)=D$ $0 = a T + v_0$ $v_0 = -a T$ and substituting this back in $s(t) = \dfrac {a t^2}{2} + (-a T) t$ $s(T) = \dfrac {a T^2}{2} + (-a T) T$ $D = -\dfrac {a T^2}{2}$ $a = -\dfrac{2 D}{T^2}$ $v_0 = - a T = \dfrac{2 D}{T}$ and you can plug your values in Thanks from topsquark Last edited by romsek; January 25th, 2017 at 11:54 AM.
January 25th, 2017, 11:36 AM   #3
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Quote:
 Originally Posted by The_Ys_Guy So I'm stuck on another homework problem. There is no equation this time to help me out and I'm unsure if I'm able to write this as function of time at this moment. Could I get another hint?
Call the initial position to be at $\displaystyle x_0 = 0 \text{ m}$. You know that the final velocity $\displaystyle v = 0 \text{ m/s}$. (Of course $\displaystyle x = 200 \text{ m}$.)

$\displaystyle x - x_0 = \frac{1}{2} (v - v_0) t$

Solve for $\displaystyle v_0$. Can you finish?

-Dan

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