We calculate the average speed of a projectile in
the absence of air resistance, a quantity that is missing from the treatment of
the problem in the literature. We then show that this quantity is equal to the
time-average instantaneous speed of the projectile, but different from its
space-average instantaneous speed. It is then shown that this behavior is
shared by general motion of all particles regardless of the dimensionality of
motion and the nature of the forces involved. The equality of average speed and
time-average instantaneous speed can be useful in situations where the
calculation of one is more difficult than the other. Thus, making it more
efficient to calculate one by calculating the other.
References
[1]
Halliday, D., Resnick, R. and Walker, J. (2005) Fundamentals of Physics. 7th Edition, Wiley, New York, 64-67.
[2]
Serway, R.A. and Jewett Jr., J.W. (2014) Physics for Scientists and Engineers. 9th Edition, Brooks/Colem Boston, 84-91.
[3]
Knight, R.D. (2008) Physics for Scientists and Engineers. 2nd Edition, Pearson/Addison-Wesley, San Francisco, 97-102.
Giambattista, A., McCarthy-Richardson, B. and Richardson, R.C. (2017) College Physics. McGraw-Hill, New York, 120-126.
[9]
Mohazzabi, P. and Kohneh, Z.A. (2005) Projectile Motion without Trigonometric Functions. The Physics Teacher, 43, 114-115. https://doi.org/10.1119/1.1855750
[10]
Barger, V.D. and Olsson, M.G. (1995) Classical Mechanics. 2nd Edition, McGraw-Hill, New York, 30-31.
[11]
Fowles, G.R. and Cassiday, G.L. (1999) Analytical Mechanics. 6th Edition, Sanders, New York, 145-153.
[12]
Mohazzabi, P. (2018) When Does Air Resistance Become Significant in Projectile Motion? The Physics Teacher, 56, 168-169. https://doi.org/10.1119/1.5025298
[13]
Mohazzabi, P. and Fields, J.C. (2004) High-Altitude Projectile Motion. Canadian Journal of Physics, 82, 197-204. https://doi.org/10.1139/p04-001
[14]
Korn, G.A. and Korn, T.M. (1968) Mathematical Handbook for Scientists and Engineers. 2nd Enlarged and Revised Edition, McGraw-Hill, New York, 943.
[15]
Stewart, J. (2016) Single Variable Calculus: Early Transcendentals. 8th Edition, Cengage, Boston, 461.
