A car traveling at 60 ft/sec begins decelerating (time is zero here, as is position) at a constant 10 feet per second squared. How many feet does the car travel before coming to a complete stop? Yet another hint: is the acceleration positive or negative? Then, determine the velocity function by integrating the acceleration function, and solving for C (the fixed point will be the velocity of the car at t=0). Integrate the velocity function to determine the position function, and solve for C (the fixed point will be the position when t=0 - and I gave that info above). One more thing...to find how long it will take to stop (which you will need in order to determine how many feet it takes to stop) you will need to use the velocity function and solve for t when v(t)=0.
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.
A car traveling at 60 ft/sec begins decelerating (time is zero here, as is position) at a constant 10 feet per second squared. How many feet does the car travel before coming to a complete stop? Yet another hint: is the acceleration positive or negative? Then, determine the velocity function by integrating the acceleration function, and solving for C (the fixed point will be the velocity of the car at t=0). Integrate the velocity function to determine the position function, and solve for C (the fixed point will be the position when t=0 - and I gave that info above). One more thing...to find how long it will take to stop (which you will need in order to determine how many feet it takes to stop) you will need to use the velocity function and solve for t when v(t)=0.
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