Positive: v(t) > 0 = motion to the right on the number line (i.e.The sign of the function tells you the direction the object is traveling. It must also meet the requirements for being a function. The function enables you to find instantaneous change as well as average change. The equation v = S/T gives you the average velocity of an object, given distance and time. Note that this is different from the velocity equation you probably came across in algebra. It tells the speed of an object and the direction (e.g. This gives you an object’s rate of change of position with respect to a reference frame (for example, an origin or starting point), and is a function of time. However, when the graph of a function is curved the change isn’t constant, and performing calculus operations becomes necessary. Finding the velocity of basic functions can be done without the use of calculus. In calculus, it is the first derivative of the position function.Īs calculus is the mathematical study of rates of change, and velocity is the measure of the change in position of an object with respect to time, the two come in contact often. Velocity, however, is defined as both the rate at which an object is traveling (i.e. In mathematics, speed refers to how fast an object travels. However, in calculus there is a significant difference between the two. You would then take that final velocity and use a kinematic equation to find Δt, either the one used above in the kinematics method or #v_f=v_i+a_yΔt#.What is the velocity of a falling object?In every day use, velocity is often used interchangeably with speed. We can see that mass cancels, as it is present on both sides, giving: Just before the rock hits the ground, it has only kinetic energy ( #h≈0#). When it is dropped, that gravitational potential energy is transformed into kinetic potential energy as it falls. at rest), for our intents and purposes it possesses only gravitational potential energy. Kinetic energy is given by #K=1/2mv^2# and gravitational potential energy is given by #U_g=mgh#.Īs the rock is not moving initially (i.e. Where #U_g# is the initial gravitational potential energy (initial and final), and #K# is the kinetic energy (initial and final). You could also use #v_f=v_i+a_yΔt# after finding the final velocity. To find the fall time, we can use this kinematic equation:īecause #y_f# and #v_(iy)# are both 0, we can rearrange to solve for Δt: Using #v_i=0# as determined above, solving for #v_f# gives:
We can use this kinematic equation to solve for the final velocity, #v_f#: Finally, because the object experiences free-fall, we know that its acceleration is equal to #-g#, or #-9.8m/s^2#. Because the object hits the ground, we can define its final height as #0# ( #y_f=0#). We are also given that it is dropped from a height of #100m# ( #y_i=100m#). Because the rock is dropped from rest, we know its initial velocity is #0# ( #v_i=0#).
This is a projectile motion problem which can be solved using kinematics. I'll give an explanation of both methods. These are just the first two that come to mind. There are at least two ways to solve this, one being with kinematics and the other with a combination of kinematics and energy conservation.