To solve this problem, we need to find the tangential and radial (centripetal) accelerations and then combine them to find the resultant acceleration.

1. First, let's find the tangential acceleration (at). Tangential acceleration is given by the formula at = r*α, where r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get at = 0.1m * 0.5 rad/sec^2 = 0.05 m/sec^2.

2. Next, let's find the radial or centripetal acceleration (ar). Centripetal acceleration is given by the formula ar = r*ω^2, where ω is the angular velocity. But we don't have ω directly, we have to find it using the formula ω = ω0 + α*t, where ω0 is the initial angular velocity (which is 0 as the wheel starts from rest), α is the angular acceleration and t is the time. Substituting the given values, we get ω = 0 + 0.5 rad/sec^2 * 2 sec = 1 rad/sec. Now, substituting ω in the formula for ar, we get ar = 0.1m * (1 rad/sec)^2 = 0.1 m/sec^2.

3. Now, we have both tangential and radial accelerations. The resultant acceleration (a) is given by the formula a = sqrt(at^2 + ar^2). Substituting the values, we get a = sqrt((0.05 m/sec^2)^2 + (0.1 m/sec^2)^2) = sqrt(0.0025 + 0.01) m/sec^2 = sqrt(0.0125) m/sec^2 = 0.1118 m/sec^2.

4. Convert this to cm/sec^2 by multiplying by 100, we get a = 11.18 cm/sec^2.

None of the options match the calculated value. There might be a mistake in the question or the options provided.

Question

To solve this problem, we need to find the tangential and radial (centripetal) accelerations and then combine them to find the resultant acceleration.

1. First, let's find the tangential acceleration (at). Tangential acceleration is given by the formula at = r*α, where r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get at = 0.1m * 0.5 rad/sec^2 = 0.05 m/sec^2.

2. Next, let's find the radial or centripetal acceleration (ar). Centripetal acceleration is given by the formula ar = r*ω^2, where ω is the angular velocity. But we don't have ω directly, we have to find it using the formula ω = ω0 + α*t, where ω0 is the initial angular velocity (which is 0 as the wheel starts from rest), α is the angular acceleration and t is the time. Substituting the given values, we get ω = 0 + 0.5 rad/sec^2 * 2 sec = 1 rad/sec. Now, substituting ω in the formula for ar, we get ar = 0.1m * (1 rad/sec)^2 = 0.1 m/sec^2.

3. Now, we have both tangential and radial accelerations. The resultant acceleration (a) is given by the formula a = sqrt(at^2 + ar^2). Substituting the values, we get a = sqrt((0.05 m/sec^2)^2 + (0.1 m/sec^2)^2) = sqrt(0.0025 + 0.01) m/sec^2 = sqrt(0.0125) m/sec^2 = 0.1118 m/sec^2.

4. Convert this to cm/sec^2 by multiplying by 100, we get a = 11.18 cm/sec^2.

None of the options match the calculated value. There might be a mistake in the question or the options provided.

Knowee AI · Accepted Answer

To solve this problem, we need to find the tangential and radial (centripetal) accelerations and then combine them to find the resultant acceleration.

1. First, let's find the tangential acceleration (at). Tangential acceleration is given by the formula at = r*α, where r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get at = 0.1m * 0.5 rad/sec^2 = 0.05 m/sec^2.

2. Next, let's find the radial or centripetal acceleration (ar). Centripetal acceleration is given by the formula ar = r*ω^2, where ω is the angular velocity. But we don't have ω directly, we have to find it using the formula ω = ω0 + α*t, where ω0 is the initial angular velocity (which is 0 as the wheel starts from rest), α is the angular acceleration and t is the time. Substituting the given values, we get ω = 0 + 0.5 rad/sec^2 * 2 sec = 1 rad/sec. Now, substituting ω in the formula for ar, we get ar = 0.1m * (1 rad/sec)^2 = 0.1 m/sec^2.

3. Now, we have both tangential and radial accelerations. The resultant acceleration (a) is given by the formula a = sqrt(at^2 + ar^2). Substituting the values, we get a = sqrt((0.05 m/sec^2)^2 + (0.1 m/sec^2)^2) = sqrt(0.0025 + 0.01) m/sec^2 = sqrt(0.0125) m/sec^2 = 0.1118 m/sec^2.

4. Convert this to cm/sec^2 by multiplying by 100, we get a = 11.18 cm/sec^2.

None of the options match the calculated value. There might be a mistake in the question or the options provided.

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