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[Mentors' note: No template because the thread was moved from the technical forums]

I have attached what my apparatus looked like, and my analysis. A metal ball is held at an height by an electromagnet. Turning off the electromagnet releases the ball, which passes through the light gates positioned at d1 and d2 respectively. When the ball passes a light gate, it records the time at which it passes.

My values of instantaneous accelerations are coming out just fine. The part where I am facing trouble is when trying to determine it from the slopes of the graphs of velocity vs time, or position vs time squares, or the square of velocity vs position.

for instance, the slope of the graph of v1^2 vs d1 (attached) is coming out to be 4.5654. Comparing this with the kinematic equation v^2 = 2gh, 2g = 4.5654, which means g = 4.5654/2, which is not even remotely close to the accepted value of g. Where am I going wrong?

**TL;DR Summary:**I need help with determining the value of 'g' using the data I have collected in the lab, using an apparatus consisting of light gates fixated on a stand, the positions of which can be varied.I have attached what my apparatus looked like, and my analysis. A metal ball is held at an height by an electromagnet. Turning off the electromagnet releases the ball, which passes through the light gates positioned at d1 and d2 respectively. When the ball passes a light gate, it records the time at which it passes.

My values of instantaneous accelerations are coming out just fine. The part where I am facing trouble is when trying to determine it from the slopes of the graphs of velocity vs time, or position vs time squares, or the square of velocity vs position.

for instance, the slope of the graph of v1^2 vs d1 (attached) is coming out to be 4.5654. Comparing this with the kinematic equation v^2 = 2gh, 2g = 4.5654, which means g = 4.5654/2, which is not even remotely close to the accepted value of g. Where am I going wrong?

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