Aparticle moves in a straight line and has acceleration given by a(t) = 12t + 10. its initial velocity is v(0) = −5 cm/s and its initial displacement is s(0) = 9 cm. find its position function, s(t).

The position function is .

Explanation:

Given that,

Acceleration

Initial velocity

Initial displacement

We know that,

The acceleration is the rate of change of velocity of the particle.

The velocity is the rate of change of position of the particle

We need to calculate the the position

The acceleration is

On integration both side

At t = 0

Now, On integration again both side

At t = 0

Hence, The position function is .

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