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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.

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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?
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January 25th, 2017, 11:32 AM   #2
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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
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Last edited by romsek; January 25th, 2017 at 11:54 AM.
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January 25th, 2017, 11:36 AM   #3
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Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by The_Ys_Guy View Post
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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