The Professor's centripetal acceleration is 0.044 m/s²
Centripetal acceleration is the acceleration of an object moving in circular motion. It is usually directed towards the center of the rotation.
It is given by:
a = v²/r
where v is the velocity and r is the radius.
Given that the radius (r) = 4 m, velocity (v) = 0.419 m/s, hence:
a = v²/r = 0.419²/4 = 0.044 m/s²
The Professor's centripetal acceleration is 0.044 m/s²
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Answer:
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Answer: F = 1235 N
Explanation: Newton's Second Law of Motion describes the effect of mass and net force upon acceleration: 
Acceleration is the change of velocity in a period of time: 
Velocity of the car is in km/h. Transforming it in m/s:

v = 13 m/s
At the moment the car decelerates, acceleration is
a = 65 m/s²
Then, force will be

= 1235 N
The horizontal net force the straps of the restraint chair exerted on the child to hold her is 1235 newtons.