Example: A tennis ball is thrown vertically upward from the ground with an initial velocityof 25 feet per second and behaves according to the equation of motion s(t)=t^3-4t^2, where s(t) is in feet and t is in seconds. Determine the following: 1. average velocity of the ball at t1=4/3 and t2= 8/3. . 2. instantaneous velocity and instantaneous acceleration at t=4/3 3. speed at t=8/3
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Example: A tennis ball is thrown vertically upward from the ground with an initial velocityof 25 feet per second and behaves according to the equation of motion s(t)=t^3-4t^2, where s(t) is in feet and t is in seconds.
Determine the following:
1. average velocity of the ball at t1=4/3 and t2= 8/3.
.
2. instantaneous velocity and instantaneous acceleration at t=4/3
3. speed at t=8/3
4. time it takes for the ball to reach the ground
5. maximum height the ball reaches
6. instantaneous velocity at the time the ball reaches the ground
7. acceleration when the ball is at its highest point and when it reaches the ground.
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