Physics
Physics
Problem
A small steel ball is projected vertically downward from the roof of a building high with an initial speed of . A student chooses the upward direction as positive for analysis. Answer the following. a. (i) Write the expressions for (a) velocity and (b) displacement of the ball as functions of time using the chosen sign convention. b. (ii) Using the expression for displacement, determine the time taken by the ball to reach the ground. c. (iii) Using the velocity–time relation, calculate the algebraic area under the – graph from until the instant of impact, and show that this area equals the displacement obtained in part (ii). Explain why the numerical value of this area is negative. d. (iv) Draw a neat velocity–time graph for the motion in your answer book and clearly mark the physical significance of the negative area under the curve.Intuitive explanation
When the student chooses upward as positive, all downward quantities—including initial velocity and displacement—become negative in the equations of motion. This sign convention flips the usual intuition, so the key is to carefully assign signs to , , and before plugging into kinematic equations. Once you're consistent with signs, the math works the same way; the challenge is tracking what negative means in context.
Intuitive explanation
When the student chooses upward as positive, all downward quantities—including initial velocity and displacement—become negative in the equations of motion. This sign convention flips the usual intuition, so the key is to carefully assign signs to , , and before plugging into kinematic equations. Once you're consistent with signs, the math works the same way; the challenge is tracking what negative means in context.