Question

Question #99084

Answer 1

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.