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Question: A car is travelling along a circular curve that has a radius of 8m. If its speed is 8 m/s and is inc...

A car is travelling along a circular curve that has a radius of 8m. If its speed is 8 m/s and is increasing uniformly at 8 m/s2, the magnitude of its acceleration at this instant is –

A

8 m/s2

B

82\sqrt{2}m/s2

C

82\frac{8}{\sqrt{2}} m/s2

D

16 m/s2

Answer

82\sqrt{2}m/s2

Explanation

Solution

a = ar2+at2\sqrt{a_{r}^{2} + a_{t}^{2}}

ar = v2r\frac{v^{2}}{r} = 828\frac{8^{2}}{8} = 8m/s2 ̃ at = 8 m/s2

\ a = 82\sqrt{2} m/s2