Question

Give precise mathematical definitions or descriptions of each

of the concepts that follow. Then illustrate the definition with

a graph or algebraic example, if possible:

the real–world interpretations of position, velocity, and

acceleration

Short answer

Position is$d=v\times t,velocity=\frac{d}{t}andacceleration=\frac{v}{t}.$

Step-by-step solution

Step 1. Given information

Position, velocity and displacement

Kinematics formula where displacement refers to area under graph of velocity and time.

Step 2. Calculation

If the position is given by function $p\left(x\right)$then the velocity of the first derivative of that function, and the acceleration is the second derivative.

Position is also called distance which can be measure through areas of (v-t) velocity time graph.

Velocity can be determined by the slope of the displacement and time (d-t) graph.

Similarly, acceleration can be determined by slope of velocity and time (v-t) graph.

$POsition=displacement=d=v\times t$where v is velocity and t refer to time.

$Velocity=\frac{d}{t}=\frac{displacement}{time}$, where d is displacement and t refer to time.

role="math" localid="1660752775622" $Acceleration=\frac{v}{t}=\frac{velocity}{time},$where v is velocity and t refer to time.

There is a formula to find the kinetic problem, where a is acceleration and t refer to time.

$v=u+at$where v is final velocity and u is initial velocity.

$s=ut+\frac{1}{2}a{t}^2$where s is displacement

$v^2=u^2+2as$

Hence, position is$d=v\times t,velocity=\frac{d}{t}andacceleration=\frac{v}{t}.$