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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-
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