Final answer:
To find the total acceleration of the propeller blade tip at 5.0 s, we combine the tangential acceleration and the centripetal acceleration. The tangential acceleration is given, and the centripetal acceleration can be found using the angular velocity, which is derived from the angular form of the uniformly accelerated motion equation.
Step-by-step explanation:
The student has asked at what the total acceleration of the tip of a propeller blade would be at t = 5.0 s, given that it starts from rest and has a constant tangential acceleration of 3.00 m/s², with the tip being 1.5 m from the axis of rotation. To find the total acceleration, we need to consider both the tangential acceleration and the centripetal acceleration at this point in time.
The tangential acceleration remains at 3.00 m/s² as it's given to be constant. To find the centripetal acceleration, we first need to determine the angular velocity after 5 seconds using the angular form of the uniformly accelerated motion, ω = αt, where α is the angular acceleration. The angular acceleration can be found by dividing the tangential acceleration by the radius, α = a_t / r, where a_t is the tangential acceleration, and r is the radius. Then, the centripetal acceleration can be calculated using a_c = rω², where r is the radius and ω is the angular velocity.
After calculating the centripetal acceleration, we then use the Pythagorean theorem to find the total acceleration by combining the tangential and centripetal accelerations. The answer will be the square root of the sum of the squares of both accelerations (a_t² + a_c²).