How are displacement, velocity, and acceleration related in describing the motion of an object?

Question

Isabella Alvarez · Accepted Answer

There are three equations for 1D motion involving displacement, velocity and constant acceleration.

There are: (i) Let #u# be the initial velocity of any object which is subjected to constant acceleration #a# for time #t#, Acceleration is rate of change of velocity, #:.# Final velocity #v# after time #t# is given as #=# Initial velocity #u# + acceleration #axx# time #t# for which acceleration acted on the object. You obtain first equation. #color(blue)(v=u+at)# (ii) Once we know the initial velocity and final velocity Average velocity #color(green)(v_(avg)=(u+v)/2)# Displacement or Distance #s# traveled in time #t# #=#Average velocity# xx #time# s=(u+v)/2 xx t# ....... (A) #=>(ut)/2+(vt)/2 # Insert the value of #v# from first equation #=>(ut)/2+((u+at)t)/2 # #=>(ut)/2+(ut)/2+(atxxt)/2 # You obtain second equation. #color(blue)(s=ut+1/2at^2) # (iii) Eliminate time #t# from the first and equation (A), to obtain third equation. #v=u+at#, taking #u# to the other side of equation to find the value of #t# #t=(v-u)/a# Insert #t# in (A) above #s=(u+v)/2 xx (v-u)/a# You get the third one as #(x+y)(x-y)=x^2-y^2# #color(blue)(v^2-u^2=2as)#

Emily Abbate · Answer

undefined Displacement, velocity, and acceleration are related concepts used to describe the motion of an object:

1. Displacement is the change in position of an object, typically measured in a straight line from the starting point to the ending point. It is a vector quantity, meaning it has both magnitude (the distance traveled) and direction.

2. Velocity is the rate of change of displacement with respect to time. It is a vector quantity that indicates both the speed (magnitude) and direction of the object's motion. Mathematically, velocity can be calculated as the derivative of displacement with respect to time.

3. Acceleration is the rate of change of velocity with respect to time. It measures how quickly an object's velocity is changing. Like velocity, acceleration is a vector quantity and can be positive, negative, or zero, depending on whether the object is speeding up, slowing down, or maintaining a constant velocity. Mathematically, acceleration can be calculated as the derivative of velocity with respect to time.

In summary, displacement describes the overall change in position, velocity describes how fast and in which direction the position is changing, and acceleration describes how quickly the velocity is changing over time. These three concepts are interconnected and provide a comprehensive understanding of the motion of an object.