## Sunday, July 4, 2010

### 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 tx and ty, after released from P. Which of the following expression gives the correct computation of acceleration?

A) 2h/( tx - ty)
B) h/( t
y2 – tx2)
C) h
2/( tx - ty)
D) 2h/( t
y2 – tx2)

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 tx and ty, the time taken t = ( ty - tx), displacement y = h, and initial velocity Vi = 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 + vi 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 + vit 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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From: TheSundayTimes, July 4, 2010, Page 7

Reference