A car moves with a speed of 30 , m/s on a cir | vedclass

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(B) Given: Tangential acceleration $a_t = 2 \, m/s^2$,velocity $v = 30 \, m/s$,and radius $r = 500 \, m$.First,calculate the centripetal acceleration

Vedclass · Accepted Answer

$2.7$

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(B) Given: Tangential acceleration $a_t = 2 \, m/s^2$,velocity $v = 30 \, m/s$,and radius $r = 500 \, m$.First,calculate the centripetal acceleration $a_c$ using the formula $a_c = \frac{v^2}{r}$.$a_c = \frac{30^2}{500} = \frac{900}{500} = 1.8 \, m/s^2$.The total acceleration $a$ is the vector sum of tangential and centripetal acceleration,given by $a = \sqrt{a_t^2 + a_c^2}$.$a = \sqrt{2^2 + 1.8^2} = \sqrt{4 + 3.24} = \sqrt{7.24}$.$a \approx 2.69 \, m/s^2$,which rounds to $2.7 \, m/s^2$.

$A$ car moves with a speed of $30 \, m/s$ on a circular path of radius $500 \, m$. If its tangential acceleration is $2 \, m/s^2$,what is the magnitude of the total acceleration of the car in $m/s^2$?

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