Acceleration from Velocity

Question

How would you find the acceleration of an automobile at $t$ seconds from the formula giving velocity $v(t)$ in $ft/sec$:

$$v(t) = \frac{85t}{6t+16}$$

$5$ seconds ? _____$ft/sec^2$

$10$ seconds ? _____$ft/sec^2$

$20$ seconds ? _____$ft/sec^2$

Do I use the formula:

$$a = \frac{v_1 - v_0}{t_1-t_0}$$

or

$$a = \frac{340}{(3t+8)^2}$$

Thanks,

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Update 1—According to comments, I should use the first derivative of the velocity equation. The answers I calculated are $.643, .235$, and $.074$. Would I need to divide by seconds?

Update 2—Thanks for all your help. The aforementioned values were correct! :D

Answer 1

I would strongly suggest that instead of simply applying formulas, you strengthen your concepts first.

The first equation you quoted:

$$a = \frac{v_1 - v_0}{t}$$

only applies in the case of a constant acceleration.

The acceleration here is not constant.

To find it you'll need to apply the more general rule:

$$a = \frac{dv}{dt}$$

which means differentiating the expression for velocity that you're given.

Answer 2

Just differentiate your velocity vector V(t) to get A(t) .Plug in 5,10,15 to get answer