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Question

A car is moving along a circular path of radius 500 m with a speed of 30 m/s. If at some instant, its speed increases at the rate of 2 m/s2, then at that instant, the magnitude of resultant acceleration will be

A
4.7 m/s2
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B
3.8 m/s2
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C
3 m/s2
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D
2.7 m/s2
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Solution

The correct option is D 2.7 m/s2
Let the tangential acceleration be at.
And let the centripetal acceleration be ac.
Centripetal acceleration, ac=v2r
=(30)2500=1.8 m/s2
Resultant acceleration at the instant
a=a2t+a2c
=(1.8)2+(2)2=2.7 m/s2

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