A small object is videotaped being thrown up into the air and coming back down.

Question

A small object is videotaped being thrown up into the air and coming back down. The video tape is analyzed and the velocity-time graph shown below was obtained. Student A considers the information in the graph and concludes that the object was initially thrown up from a distance of 23 meters and shows that the vertical acceleration was negative on it's way up, zero at the top, and negative on the way down. This proves that free fall acceleration is always negative accept at the top of the trajectory. Student B disagrees and states that "23" on the y-axis represents the initial velocity and that the slope of the graph proves that the vertical acceleration of an object in free fall (neglecting air resistance) is always -9.8 m/s2 even at the top of the trajectory. What aspect of student A's statement is correct, if any, and explain. What aspect of student B's statement is correct, if any, and explain. What aspect of student A's statement is wrong, if any, and explain. What aspect of student B's statement is wrong, if any, and explain.

Explanation / Answer

Student A was correct : Vertical acceleration zero at the top

Reason: Object was thrown up at a velocity of 23m/s with some acceleration(g), at hightes point that acceleration nullifies the acceleration due to gravity, so net verical accleration is zero.

Student B was correct :23 is the initial velocity.

Reason: its a Velocity vs time graph to y axis shows velocity.

Student A wrong at :23 as distance, vertical acceleration was negative in up and down movement, g always negative except at top of trajectory.

Reason: 23 is the velocity

negative or positive value of acceleration depends on the refrence we are taking, if we are taking its positve upwards as per graph them downwards it will be negative.

value of g also depends on reference we are taking. and at the top of trajectory velocity is zero but acceleration is "g"

Student B wrong : Slop shows that verical acceletation is always -9.81

Reason : this graph have reference of up positive and down negative, so in this graph only vertical acceleration is -9.81, rest it will depend on the reference. At the top acceleration value will be g.

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