An object is at rest at #(2 ,9 ,5 )# and constantly accelerates at a rate of #1/5 m/s# as it moves to point B. If point B is at #(6 ,2 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
Jul 29, 2017

Answer:

#t = 9.11# #"s"#

Explanation:

NOTE: I'll assume the given acceleration is #1/5# #"m/s"^2#, not #1/5# #"m/s"#.

We're asked to find the time #t# it takes an object to travel a certain distance with a given constant acceleration.

To do this, we can use the equation

#Deltax = v_(0x)t + 1/2a_xt^2#

where

  • #Deltax# is the distance it travels, which can be found using the distance formula:

#Deltax = sqrt((6-2)^2 + (2-9)^2 + (7-5)^2) = 8.31# #"m"#

  • #v_(0x)# is the initial velocity, which is #0# since it started from rest

  • #t# is the time (we're trying to find this)

  • #a_x# is the constant acceleration (given as #1/5# #"m/s"^2#)

Plugging in known values, we have

#8.31# #"m"# #=0t + 1/2(1/5color(white)(l)"m/s"^2)t^2#

#t = sqrt((8.31color(white)(l)"m")/(1/10color(white)(l)"m/s"^2)) = color(red)(ul(9.11color(white)(l)"s"#