Answer to Question #203845 in Calculus for Faten

Question

Explain the relationship between distance, velocity, acceleration and time using calculus.

Answer 1

Velocity is the measure of amount of distance an object covers in a given amount of time ,here is an equation that relates the relationship between distance velocity an time .

Velocity equals to distance travelled divided by the time an object takes to get there.

The relationship between velocity and time is simple one during uniformely accelerated straight-line motion ,the longer the acceleration the greater the change in velocity not forgetting velocity is directly proportional to time when acceleration is constant

Also acceleration (a) is the change in velocity$\Delta$v over change in time $\Delta$t,represented by the equation

a=$\Delta$ v/$\Delta$ t. These allows to measure how first velocity change in m/s²,acceleration also covers the a vector quantity so it includes magnitude and direction

Distance (s) - velocity (v) = differentiate the distance function dy/dx=f(s)

Velocity (v) - acceleration (a)=differentiate velocity function dy/dx=f(v)

Acceleration (a) - velocity (v) =integrate acceleration function $\intop$ f(a')

Velocity (v) - distance (s) =integrate the velocity function $\intop$f (v')