Question

an object after travelling at a uniform velocity of 4m/s for 5s, travels with a constant acceleration of 0.5 m/s in the same direction for another 5s. find the average velocity throughout the journey.​

Answer 1

$\huge\sf\pink{Answer}$

☞ Average Velocity is 4.625 m/s

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$\huge\sf\blue{Given}$

✭ Initial Velocity (u) = 4 m/s

✭ Acceleration (a) = 0.5 m/s

✭ Time¹ & Time² (T)= 5 Sec

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$\huge\sf\gray{To \:Find}$

◈ Average Velocity through the journey?

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$\huge\sf\purple{Steps}$

Case 1

We know that,

$\underline{\boxed{\sf Velocity = \dfrac{Displacement}{Time}}}$

Substituting the given values,

➝ $\sf Velocity = \dfrac{Displacement}{Time}$

➝ $\sf Velocity \times Time = Displacement$

➝ $\sf 4\times 5 = Displacement$

➝ $\sf \green{Displacement = 20 \ m}$

Case 2

As per the third equation of motion,

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

Substituting the given values,

➳ $\sf s = ut+\dfrac{1}{2} at^2$

➳ $\sf s = 4\times 5 + \dfrac{1}{2} \times 0.5 \times 5^2$

➳ $\sf s = 20+\dfrac{1}{2} \times 0.5 \times 25$

➳ $\sf s = 20+6.25$

➳ $\sf \red{Displacement =26.25 \ m}$

So now we know that Total Distance is,

➢ $\sf D_1 + D_2$

➢ $\sf 20+26.25$

➢ $\sf Total \ Displacement = 46.25$

Now average velocity is given by,

$\underline{\boxed{\sf Avg \ Velocity = \dfrac{Total \ Displacement}{Total \ Time}}}$

Substituting the values,

»» $\sf Avg \ Velocity = \dfrac{Total \ Displacement}{Total \ Time}$

»» $\sf Avg \ Velocity = \dfrac{46.25}{5+5}$

»» $\sf Avg \ Velocity = \dfrac{46.25}{10}$

»» $\sf \orange{Avg \ Velocity = 4.625 \ m/s}$

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Answer 2

Answer:

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