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I have a couple of graphs, one showing position, and the other showing velocity, both with respect to time. I have got my $x$, $t$, $v$, $v_0$, $x_0$, $t_0$ from them. I need to calculate the acceleration due to friction. However, I'm not sure if I should be using the change in velocity divided by change in time to calculate it or use this other equation I have.

$$ x(t)=(x_0-v_0t_0+\frac{1}{2}at_0^2)+(v_0-at_0)t+\left(\frac{1}{2}a \right)t^2$$

I've got different answers using each and I'm not sure which I need.

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This equation for $x(t)$ is unlikely to be helpful, if I am understanding your question correctly.

Acceleration is the rate of change of velocity, so the acceleration due to friction is the change in velocity due to friction divided by the time elapsed during that change. We may need more information to really help you, but with what you have told us, the acceleration due to friction (assuming it is the only force acting on the system between times $t$ and $t_0$) will be $\frac{v-v_0}{t-t_0}$. Please provide more information if this is not helpful.

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  • $\begingroup$ It's for the situation of a cart moving in a fixed direction along a track attached to a spring that gets stretched and then let go causing the cart to move. I had a feeling that the change in v over change in t would be more fitting but I was given the other equation so I and hadn't found another use for it yet so I thought that I might have to use that. $\endgroup$
    – windy401
    Commented Feb 15, 2017 at 16:00
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    $\begingroup$ If $t_0$ is the time at which the cart is released from the spring, the answer I gave above will be correct because from that point on, friction will be the only force acting on the cart. $\endgroup$ Commented Feb 15, 2017 at 16:50

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