Question

the acceleration of a particle is given by a=3t2+2t+2 ms2 if initial velocity at t=0 is 2m/s.find the velocity at the end of 2s

Answer 1

Answer:

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Answer 2

FINAL VELOCITY IS 18 m/s .

Given:

• a = 3t² + 2t + 2

• at t = 0 , u = 2 m/s

To find:

• Final velocity at t = 2 sec ?

Calculation:

$a = 3 {t}^{2} + 2t + 2$

• Now, we know that :

$\implies \: \dfrac{dv}{dt} = 3 {t}^{2} + 2t + 2$

$\implies \: dv=( 3 {t}^{2} + 2t + 2) \: dt$

• Integration on both sides:

$\implies \displaystyle\int_{2}^{v} dv=\int_{0}^{2}( 3 {t}^{2} + 2t + 2) \: dt$

$\implies v - 2= {t}^{3} + {t}^{2} + 2t \bigg | _{0}^{2}$

$\implies v - 2= 8 + 4 + 4$

$\implies v =18 \: m {s}^{ - 1}$

So, final velocity is 18 m/s