A jeep travelling at a constant speed of 108 km/hr rounds a curve of radius 100 m. Find its acceleration.
Correct answer: E. 9 m/s2
- A. 3 m/s2
- B. 6 m/s2
- C. 7 m/s2
- D. 8 m/s2
- E. 9 m/s2
Explanation
The correct answer is 9 m/s2. To find the acceleration of the jeep as it rounds the curve, we use the formula for centripetal acceleration: a = v2 / r, where 'v' is the velocity and 'r' is the radius of the curve. The velocity is given as 108 km/hr, which must be converted to meters per second by dividing by 3.6, resulting in 30 m/s. Substituting into the formula: a = (30 m/s)2 / 100 m = 9 m/s2. The other options are incorrect because they arise from either incorrect unit conversion or misapplication of the centripetal acceleration formula.
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Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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