Question

A car accelerates uniformly from an initial velocity of 2m/s to a final velocity of 10m/s in 8 seconds it then slows down uniformly ti a final velocity of 4m/s in 6 seconds calculate the acceleration of the car during the first 8 seconds and during last 6 seconds
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Answer 1

$\huge\sf\pink{Answer}$

☞ Acceleration in case 1 is 1 m/s²

☞ Acceleration in case 2 is -1 m/s²

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$\huge\sf\blue{Given}$

✭ Initial Velocity = 2 m/s

✭ Final Velocity₁ = 10 m/s

✭ Time₁ = 8 sec

✭ Final Velocity₂ = 4 m/s

✭ Time₂ = 6 seconds

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

◈ Acceleration of the car during T₁ & T₂?

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$\huge\sf\purple{Steps}$

So we shall find the acceleration of the bidu with the help of the first Equation of motion, that is,

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

Case 1

• Initial velocity (u) = 2 m/s
• Final velocity (v) = 10 m/s
• Time (t) = 8 sec

Substituting the values,

➝ $\sf v = u+at$

➝ $\sf 10 = 2+a\times 8$

➝ $\sf 10-2 = 8a$

➝ $\sf 8 = 8a$

➝ $\sf \dfrac{8}{8} = a$

➝ $\sf \red{Acceleration_1 = 1 \ m/s^2}$

Case 2

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 4 m/s
• Time = 6 sec

Substituting the Values,

➳ $\sf v = u+at$

➳ $\sf 4 = 10+a\times 6$

➳ $\sf 4-10 = 6a$

➳ $\sf -6 = 6a$

➳ $\sf \dfrac{-6}{6} = a$

➳ $\sf \orange{Acceleration_2 = -1 \ m/s^2}$

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