Aparticle is moving with the given data. find the position of the particle. a(t) = 2t + 9, s(0) = 8, v(0) = −7

Rate of change of velocity with respect to time is known as acceleration.

Position of particle is given by,  

Given data are,   a(t) = 2t + 9, s(0) = 8, v(0) = −7

Since, Rate of change of velocity with respect to time is known as acceleration.

Integrating both side.

We get,  

Substituting v(0)= -7 in above equation

We get,   c = -7

So,  

Since,  

    Integrating both side

We get,  

Substituting s(0)=8 in above equation.

 We get,   c = 8

So, position of particle becomes,

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1