A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?

a = vf - vi
t

1 Answer
Aug 3, 2017

Answer:

#"acceleration" = 7.33# #"m/s"#

Explanation:

We're asked to find the (constant) acceleration of the roller coaster, given its final and initial velocities.

To do this, we can use the kinematics equation

#ul(v_x = v_(0x) + a_xt#

where

  • #v_x# is the final velocity

  • #v_(0x)# is the initial velocity

  • #a_x# is the acceleration (what we're trying to find)

  • #t# is the time interval

We know:

  • #v_x = 32# #"m/s"#

  • #v_(0x) = 10# #"m/s"#

  • #a_x = ?#

  • #t = 3# #"s"#

Plugging in known values:

#32# #"m/s"# #= 10# #"m/s"# #+ a_x(3color(white)(l)"s")#

#a_x = (32color(white)(l)"m/s" - 10color(white)(l)"m/s")/(3color(white)(l)"s") = color(red)(ulbar(|stackrel(" ")(" "7.33color(white)(l)"m/s"^2" ")|)#