A propeller blade at rest starts to rotate from t = 0 s to t = 5.0 s with a tangential acceleration of the tip of the blade at 3.00 m/s2. The tip of the blade is 1.5 m from the axis of rotation. At t = 5.0 s, what is the total acceleration of the tip of the blade?

Explanation:

Given that

Tangential acceleration (at) =3m/s²

The propeller blade starts from rest i.e. wo=0rad/sec

And also the change in time ∆t=5sec

Also radius of blade (r)=1.5m

We have the tangential acceleration, so we need the centripetal acceleration

Which is given as

ac=v²/r

Then we need to get the final velocity using equation of motion

v=u+at

Where (a) is the tangential acceleration = 3m/s²

And the is final time at t=5sec

v=0+3×5

v=0+15

v=15m/s

Then, ac=v²/r

ac=15²/1.5

ac=150m/s²

Then, the total acceleration is given as

a=√(at)²+(ac)²

Since at=3m/s² and ac=150m/s²

Then,

a=√3²+150²

a=√22509

a=150.03m/s²

The total acceleration is 150.03m/s²

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