Secondary 4 Preliminary Examination Physics (18th September 2008)

From: MARIS STELLA HIGH SCHOOL, Secondary 4 Preliminary Examination 2, PAPER 1 MULTIPLE CHOICE, NO. 3, 18th September 2008

The acceleration of free fall is determined by timing the fall of a steel ball photo-electrically. The ball passes X and Y at times t_x and t_y, after released from P. Which of the following expression gives the correct computation of acceleration?

A) 2h/( t_x - t_y)
B) h/( t_y² – t_x²)
C) h²/( t_x - t_y)
D) 2h/( t_y² – t_x²)


Solution:








To obtain the displacement, we have to integrate the eq ④


With reference to the diagram above, to compute the acceleration, g, between time t_x and t_y, the time taken t = ( t_y - tx), displacement y = h, and initial velocity V_i = Vx

Substituting into eq ⑤





Supporting Explanations
Source: http://www.school-for-champions.com/science/gravity_equations_derivation.htm

Overview of distance and time relationships

The displacement a falling object travels in a given time is found by knowing that velocity is the change in displacement with respect to time:

v = dy/dt

Substituting for v in the equation v = gt + v_i and integrating, we get:

y = gt2/2 + vit

Note: Sincethe convention is that down is a positive direction, the downward distance y from the starting point is also positive.

Rearranging y = gt²/2 + v_it and solving the quadratic equation for t gives you:

t = [ −vi± √(vi2+ 2gy) ]/g

This equation can create some confusion because of the plus-or-minus sign. If the object is thrown downward, the plus (+) sign is used. If the object is thrown upward, the sign depends on the object's position with respect to the starting point.

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Reference

• MARIS STELLA HIGH SCHOOL, Secondary 4 Preliminary Examination 2, PAPER 1 MULTIPLE CHOICE, NO. 3, 18th September 2008
• http://www.school-for-champions.com/science/gravity_equations_derivation.htm