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Chapter 2: Problem 51

A particle moving in a straight line has velocity and displacement equation as \(v=4 \sqrt{1+s}\), where \(v\) is in \(\mathrm{m} / \mathrm{s}\) and \(s\) is in \(\mathrm{m}\). The initial velocity of the particle is (A) \(4 \mathrm{~m} / \mathrm{s}\) (B) \(16 \mathrm{~m} / \mathrm{s}\) (C) \(2 \mathrm{~m} / \mathrm{s}\) (D) Zero

Short Answer

Expert verified
The initial velocity of the particle can be found by plugging \(s=0\) into the given velocity equation \(v = 4\sqrt{1+s}\). After substituting and simplifying, we find that the initial velocity is 4 m/s. Therefore, the correct answer is (A) \(4 \mathrm{~m} / \mathrm{s}\).

Step by step solution

01

Substitute displacement value

In order to find the initial velocity, we will substitute the value of \(s=0\) into the given velocity equation \(v = 4\sqrt{1+s}\): \(v = 4\sqrt{1+0}\)
02

Simplify the equation

Now, we can simplify the equation to find the initial velocity: \(v = 4\sqrt{1}\) Since the square root of 1 is just 1, we have: \(v = 4(1)\)
03

Calculate initial velocity

Finally, we can calculate the initial velocity of the particle: \(v = 4\) The initial velocity of the particle is 4 m/s. Therefore, the correct option is (A) \(4 \mathrm{~m} / \mathrm{s}\).

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