Question #99084

1 Answer
Aug 17, 2017

Not a full explanation, but a quick example relating the two subjects:

Explanation:

Acceleration is the rate at which velocity changes with respect to time, and is a vector quantity:

veca = (dvecv)/(dt) = lim_(Deltatrarr0) (Deltavecv)/(Deltat)

If the acceleration is constant, we can use the equations of motion with constant acceleration to solve many kinematics problems.

For example, say we have a car originally traveling at 20 "m/s", and comes to a stop (under constant acceleration) in 0.5 "s". We can use the equation

ul(v_x= v_(0x) + a_xt

to find the acceleration, a_x, where

  • v_x is the final velocity (which is 0 since it comes to a stop)

  • v_(0x) is the initial velocity of the car (given as 20 "m/s")

  • t is the time interval (given as 0.5 "s")

We can plug in these values to find the acceleration of the car:

0 = 20color(white)(l)"m/s" + a_x(0.5color(white)(l)"s")

color(red)(ul(a_x = -40color(white)(l)"m/s"^2

Newton's second law relates the acceleration of a body to the net force acting on it:

ul(sumvecF = mveca

(m is the mass of the object)

For example, if the car in the previous problem had a mass of 75 "kg", the net force acting on the car would be

sumF = (75color(white)(l)"kg")(color(red)(-40color(white)(l)"m/s"^2)) = color(blue)(ul(3000color(white)(l)"N"

This wasn't a full, in-depth explanation of these concepts, but an example always helps clarify things.

You can actually visit one of my scratchpads here for further information about the constant-acceleration equations and how they are derived.