Calc Q: Find Acceleration Using Velocity Function

• bah
In summary, the conversation discusses using the velocity function to find acceleration. The velocity of a falling body is given by v=8sqrt(s-t)+1 feet per second, and the derivative of this function is acceleration. By substituting the given equation for v in the second equation, it can be shown that the body's acceleration is 32 ft/sec^2.
bah
Calculus Question. Using velocity function to find acceleration?

The velocity of a falling body is v=8sqrt(s-t)+1 feet per second at the instant t(sec) the body has fallen s feet from its starting point. Show that the body's acceleration is 32 ft/sec^2.

Well, the derivative of the velocity function is acceleration, so it's v'=4(v-1)(s-t)^(-1/2)

How do I go from there?

Last edited:
I don't know. The RHS of the given equation doesn't have a proper dimension.

Well, you know that:
$$v=8\sqrt{s-t}+1$$
so you could substitute that in for the $v$ in the second equation:
$$v'=4\frac{v-1}{\sqrt{s-t}}$$
It should work out nicely from there.

What is the purpose of finding acceleration using the velocity function?

The purpose of finding acceleration using the velocity function is to determine the rate at which an object's velocity is changing over time. This information can be used to understand the motion of an object and make predictions about its future movement.

How do you find acceleration using the velocity function?

To find acceleration using the velocity function, you can use the formula a(t) = v'(t) = d/dt(v(t)), where v'(t) represents the derivative of the velocity function with respect to time. This will give you the instantaneous acceleration at a specific time t.

What units are used to measure acceleration?

Acceleration is typically measured in units of distance per time squared, such as meters per second squared (m/s^2) or feet per second squared (ft/s^2). This represents the change in velocity over a specific time interval.

How is acceleration related to velocity and displacement?

Acceleration is the rate of change of velocity, which means it is the derivative of the velocity function. It is also related to displacement through the equation a(t) = v'(t) = d/dt(v(t)) = d^2/dt^2(x(t)), where x(t) is the displacement function.

What can we learn from the acceleration vs. time graph?

The acceleration vs. time graph can provide valuable information about an object's motion. The slope of the graph represents the rate of change of acceleration, which can help us understand how an object's velocity is changing over time. Additionally, the area under the graph can give us the displacement of the object over a specific time interval.

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