How Do Velocity and Acceleration Change When a Ball Falls?

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SUMMARY

A ball falling from a height of 16 meters reaches the ground in 4.0 seconds, resulting in a final velocity of 4.0 m/s downward. However, this calculation incorrectly applies the formula for constant speed rather than accounting for gravitational acceleration. The correct acceleration of the ball is 9.81 m/s² downward, which is the standard acceleration due to gravity on Earth. This highlights the importance of using appropriate kinematic equations for objects in free fall.

PREREQUISITES
  • Understanding of kinematic equations
  • Knowledge of gravitational acceleration (9.81 m/s²)
  • Familiarity with the concept of free fall
  • Basic algebra for solving equations
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  • Study the kinematic equation: \( v = u + at \)
  • Learn about free fall and its implications in physics
  • Explore the differences between constant speed and accelerated motion
  • Investigate how to calculate displacement using \( d = ut + \frac{1}{2}at^2 \)
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1. A ball falls from rest from a height of 16 m and hits the ground after 4.0 s.
(a) What was the velocity of the ball after 4.0 seconds?
(b) What is the acceleration of the ball?


Homework Equations





The Attempt at a Solution


(a) v=d/t = 16m/4.0s = 4.0 m/s (down)
(b) a = v2-v1/t = 4.0m/s-0.0m/s/4.0 s = 1.0m/s/s
 
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Unless we are dealing some other planet here, you know the acceleration is 9.81 m/s^2 downward. So you can't use v =d/t, which is a constant speed formula.
 

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