A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

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A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

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Answer 1 · 2018-04-09T12:51:35

Centripetal acceleration $a_{c}$ $a_c$ is given by the expression

$a_{c} = R ω^{2} = \frac{v^{2}}{R}$ $a_c=Romega^2=v^2/R$
where $v$ $v$ is linear velocity of the object, $ω$ $omega$ is its angular velocity and $R$ $R$ is the radius of the circle in which object moves.

Tangential acceleration $a_{t}$ $a_t$ is given to be $=0.500\ ms^-2$

Equating the magnitudes of two and inserting value of $R$ we get

$v^2/400=0.500$
$=>v=sqrt(0.500xx400)=sqrt200=14.142\ ms^-1$

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A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

1 Answer

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