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?

Answer 1

acceleration = #1/2#

The velocity, #v#, is defined as #v=(ds)/dt#, and the acceleration, #a# is given by #a=(dv)/dt#
We are told that #v=sqrt(s) #
# :. (dv)/(ds) = 1/2s^(-1/2) # # " " = 1/(2sqrt(s)) #

So using the chain rule we can write:

# a = (dv)/dt# # \ \ = (dv)/(ds) * (ds)/dt# # \ \ = (1/(2sqrt(s))) * v# # \ \ = (1/(2sqrt(s))) * sqrt(s)# # \ \ = 1/2#
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Answer 2

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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Answer from HIX Tutor

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.

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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