Question #99084

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.