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Asked By :  Priyans
Answers1

a car is moving along a circular road at a speed of 20 ms the

a car is moving along a circular road at a speed of 20 ms the radius of circular road is 10 m if the speed is increased at the rate of 30 ms what is the resultant acceleration at that moment a 10 ms b 50 ms 250 ms d 80 ms



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To find the resultant acceleration of the car, we need to consider both the centripetal (radial) acceleration and the tangential acceleration.

  1. Centripetal Acceleration (a_c): The formula for centripetal acceleration is: ac=v2ra_c = \frac{v^2}{r} Where:
  • vv is the speed of the car (20 m/s)
  • rr is the radius of the circular road (10 m)

ac=20210=40010=40m/s2a_c = \frac{20^2}{10} = \frac{400}{10} = 40 \, \text{m/s}^2

  1. Tangential Acceleration (a_t): The tangential acceleration is given as 30 m/s².

  2. Resultant Acceleration (a_r): To find the resultant acceleration, combine the centripetal and tangential accelerations using the Pythagorean theorem, since they are perpendicular to each other:

ar=ac2+at2a_r = \sqrt{a_c^2 + a_t^2} ar=402+302a_r = \sqrt{40^2 + 30^2} ar=1600+900a_r = \sqrt{1600 + 900} ar=2500a_r = \sqrt{2500} ar=50m/s2a_r = 50 \, \text{m/s}^2

So, the resultant acceleration is 50m/s250 \, \text{m/s}^2.

Therefore, the correct answer is 50m/s2\boxed{50 \, \text{m/s}^2}.


Answered By

Daniel Curry

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