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  4. A car is moving on circular track of radius 150 m and at some time its speed is decreasing at a rate of 8 m / s 2, if the speed of car at that instant was 30 m / s, net acceleration of the car will be

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Q. A car is moving on circular track of radius $150\, m$ and at some time its speed is decreasing at a rate of $8\, m / s ^{2}$, if the speed of car at that instant was $30\, m / s$, net acceleration of the car will be

Solution:

$a_{c}=\frac{v^{2}}{r}=\frac{30 \times 30}{150}=6\, m / s ^{2}$
$a_{t}=8\, m / s ^{2}$
both accelerations are always perpendicular
$a=\sqrt{a_{c}^{2}+a_{t}^{2}}=\sqrt{(6)^{2}+(8)^{2}}$
$=10\, m / s ^{2}$