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Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 7 cos(t)i 6 sin(t)j v(t) = a(t) = |v(t)| =

Sagot :

The velocity, acceleration and speed are -

v(t) = - 7sin t [tex]i[/tex] + 6cos t [tex]j[/tex]

a(t) =  - 7cos t [tex]i[/tex] - 6sin t [tex]j[/tex]

s(t) =  [tex]\sqrt{(7cos\;t) ^{2} +(6sin\;t)^{2} }[/tex]

We have the position vector → r(t) = 7cos(t) i +  6sin(t) j

We have to determine the velocity, acceleration and speed of particle.

What is the formula to calculate the instantaneous velocity and acceleration of object ?

The instantaneous velocity and acceleration can be calculated using -

v = [tex]$\frac{dx}{dt}[/tex]

a = [tex]$\frac{dv}{dt}[/tex]

According to the question, we have -

r(t) = 7cos(t) i +  6sin(t) j

The velocity can be calculated using -

v(t) = [tex]$\frac{dr(t)}{dt} = \frac{d}{dt}\;(7 cos\;t \;i + 6 sin\;t\;j)[/tex] = - 7sin t [tex]i[/tex] + 6cos t [tex]j[/tex]

The acceleration can be calculated using -

a(t) = [tex]$\frac{dv(t)}{dt} = \frac{d}{dt}\;(-7 sin\;t \;i + 6 cos\;t\;j)[/tex] = - 7cos t [tex]i[/tex] - 6sin t [tex]j[/tex]

The speed at time t can be found out as follows -

|r(t)| = [tex]\sqrt{(7cos\;t) ^{2} +(6sin\;t)^{2} }[/tex]

Hence, the velocity, acceleration and speed are -

v(t) = - 7sin t [tex]i[/tex] + 6cos t [tex]j[/tex]

a(t) =  - 7cos t [tex]i[/tex] - 6sin t [tex]j[/tex]

s(t) =  [tex]\sqrt{(7cos\;t) ^{2} +(6sin\;t)^{2} }[/tex]

To solve more questions on Vector Kinematics, visit the link below-

https://brainly.com/question/13669106

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