Question

A baseball starts from rest and rolls 50.0 m down a hill in 10.0 seconds. What is the acceleration? What is the velocity after 10 seconds?

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Initial Velocity (u) = 0 m/s

✭ Distance (s) = 50 m

✭ Time (t) = 10 sec

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Acceleration & the final velocity of the baseball?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Here we shall use the second Equation of motion to find the acceleration of the body, that is,

$\displaystyle\sf \underline{\boxed{\sf s = ut+\dfrac{1}{2}at^2}}$

And the first Equation of motion to find the velocity of the body, that is,

$\displaystyle\sf \underline{\boxed{\sf v = u+at}}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

On finding the acceleration of the body,

➝ $\displaystyle\sf s = ut+\dfrac{1}{2}at^2$

➝ $\displaystyle\sf 50 = 0\times 10+\dfrac{1}{2}\times a\times 10^2$

➝ $\displaystyle\sf 50 = \dfrac{1}{2}\times a\times 100$

➝ $\displaystyle\sf 50 = 50a$

➝ $\displaystyle\sf \dfrac{50}{50} = a$

➝ $\displaystyle\sf \orange{Acceleration = 1 \ m/s^2}$

Now the Final Velocity of the body will be,

➳ $\displaystyle\sf v = u+at$

➳ $\displaystyle\sf v = 0+1\times 10$

➳ $\displaystyle\sf\pink{v = 10 \ m/s}$

$\displaystyle\sf \underline{\therefore\sf Acc^n \ is \ 1 m/s^2 \ \& \ Fv \ is \ 10 m/s}$

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Answer 2

Given

✭ Initial Velocity (u) = 0 m/s

✭ Distance (s) = 50 m

✭ Time (t) = 10 sec

$\displaystyle\huge\underline{\sf\orange{To \ Find}} </p><p>$

◈ Acceleration & the final velocity of the baseball?

$\displaystyle\large\underline{\sf\orange{Solution}} </p><p></p><p>$

Here we shall use the second Equation of motion to find the acceleration of the body, that is,

$\displaystyle\sf \underline{\boxed{\sf s = ut+\dfrac{1}{2}at^2}} </p><p>$

And the first Equation of motion to find the velocity of the body, that is,

$\displaystyle\sf \underline{\boxed{\sf v = u+at}} </p><p></p><p>$

━━━━━━━━━

$\underline{\bigstar\:\textsf{According to the given Question :}}$

On finding the acceleration of the body,

$➝ \begin{gathered}\displaystyle\sf s = ut+\dfrac{1}{2}at^2\\\end{gathered} </p><p>$

$➝ \begin{gathered}\displaystyle\sf 50 = 0\times 10+\dfrac{1}{2}\times a\times 10^2\\\end{gathered} </p><p>$

$➝ \begin{gathered}\displaystyle\sf 50 = \dfrac{1}{2}\times a\times 100\\\end{gathered} </p><p>$

$➝ \begin{gathered}\displaystyle\sf 50 = 50a\\\end{gathered} </p><p>$

$➝ \begin{gathered}\displaystyle\sf \dfrac{50}{50} = a\\\end{gathered} </p><p>$

$➝ \displaystyle\sf \orange{Acceleration = 1 \ m/s^2}$

Now the Final Velocity of the body will be,

$➳ \begin{gathered}\displaystyle\sf v = u+at\\\end{gathered}$

$➳ \begin{gathered}\displaystyle\sf v = 0+1\times 10\\\end{gathered} </p><p>$

$➳ \displaystyle\sf\pink{v = 10 \ m/s} \\ </p><p></p><p>\displaystyle\sf \underline{\therefore\sf Acc^n \ is \ 1 m/s^2 \ \& \ Fv \ is \ 10 m/s} </p><p>$

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