How galileo proved that the acceleration of freely falling bodies is same

An alligator swims to the left with a constant velocity of 5 \,\dfrac{\text{m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction. when the alligator sees a bird straight ahead, the alligator speeds up with a constant acceleration of 3 \,\dfrac{\text {m}}{\text s^2}3 s 2 m ? 3, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward until it reaches a final velocity of 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction leftward. how many seconds does it take the alligator to speed up from 5 \,\dfrac{\text {m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction to 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction?

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Determine the age of a fossil if it had only one eighth of its original carbon-14 content remaining?