An object's two dimensional velocity is given by $v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )$ . What is the object's rate and direction of acceleration at $t=5$ ?

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An object's two dimensional velocity is given by $v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )$ . What is the object's rate and direction of acceleration at $t=5$ ?

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Answer 1 · 2017-03-13T17:25:37

Given that object's two dimensional velocity is
$v(t)=(tsin(π/3t),2cos(π/2t)−3t)$ .

Acceleration $a(t)=dotv(t)=d/dt(tsin(π/3t),2cos(π/2t)−3t)$
$=>a(t)=(tpi/3cos(π/3t)+sin(pi/3t),-2pi/2sin(π/2t)−3)$

Required acceleration at $t=5$ is
$a(5)=((5pi)/3cos((5π)/3 )+sin((5pi)/3 ),-pisin((5π)/2 )−3)$
$=>a(5)=((5pi)/3xx1/2-sqrt3/2,-(pi+3))$
$=>a(5)=(1.75197, -6.14159)$

$|a(5)|=sqrt((1.75197)^2+(-6.14159)^2)$
$|a(5)|=6.3866" units"$

Direction is given by
$alpha=tan^-1(-6.14159/1.75197)=-74.08^@$

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An object's two dimensional velocity is given by $v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )$ . What is the object's rate and direction of acceleration at $t=5$ ?

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An object's two dimensional velocity is given by v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t ). What is the object's rate and direction of acceleration at t=5 t=5 ?

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An object's two dimensional velocity is given by $v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )$ . What is the object's rate and direction of acceleration at $t=5$ ?