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A particle is moving along a straight line and has acceleration given by a(t) = 20t^3+12t^2}....

A particle is moving along a straight line and has acceleration given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m / s and its initial displacement is s( 0 ) = 5 m. Find the position of the particle at t = 1 seconds.

Math   Calculus   
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Answer #1

Solution-

The acceleration of the particle and data are given

Use the acceleration of the particle to find displacement at time t=1 s,

Find antiderivative of acceleration (velocity) and apply boundary condition at t=0

Find the antiderivative of velocity (displacement) and apply boundary condition at t=0,

substitute,

Now, find the position of the particle at t=1 s,

Therefore, the position of the particle after 1 second is 7.

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