# An object moves in such a way that when it has moved a distance s its velocity is #v=sqrts#, how do you find its acceleration?

acceleration =

So using the chain rule we can write:

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To find the acceleration, differentiate the velocity function with respect to time. The velocity function is v = √s. Differentiate v with respect to time (t) to find acceleration (a):

dv/dt = d(√s)/dt

Using the chain rule:

dv/dt = (1/2)(s^(-1/2))(ds/dt)

Given that v = √s, differentiate both sides with respect to time:

dv/dt = (1/2)(s^(-1/2))(ds/dt) = (1/2)(s^(-1/2))(ds/dt) = (1/2)(1/√s)(ds/dt)

We know that ds/dt represents the rate of change of distance with respect to time, which is velocity (v). So, ds/dt = v.

Substitute ds/dt with v:

dv/dt = (1/2)(1/√s)(v)

Now, we have an expression for acceleration (dv/dt) in terms of velocity (v) and distance (s):

a = dv/dt = (1/2)(1/√s)(v) = (1/2)(1/√s)(√s) = 1/2

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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