Question

can u guys pls answer this Q with correct step by step explanation..plss..
-> Q - If a car accelerates with acceleration depends on displacement as a = 6x² + 2x + 5. Find the velocity particles when it is at x = 3 m. Given initially it starts from x = 1 with velocity 2 m/s ?​

Answer 1

We have,

• Initial velocity of car = 2 m/s
• Intial distance = 1 m
• Final distance = 3 m
• Accleration of the car = 6x² + 2x + 5

Let us first, find the acceleration produced, at intial starting;

• Put x = 1

= 6x² + 2x + 5

= 6(1)² + 2(1) + 5

= 6 + 2 + 5

= 8 + 5

= 13 m/s-²

Now, we have accleration = 13 m/s-², now using the 3rd equation of motion;

= 2as = v² - u²

= 2( 13 )(3) = v² - (2)²

• I have taken s = 3 because we need to find the final velocity on covering 3 m and I have taken u = 20 as per mentioned in the question.

= 78 = v² - 4

= 78 + 4 = v²

= √82 = v

= 9.05 = v - - - - - - - {nearly equal to 9 m/s}

Therefore, the final velocity of the car will be 9.05 m/s.

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Thank youu!! :)) $\;$