An object is at rest at #(2 ,1 ,5 )# and constantly accelerates at a rate of #7/6 m/s# as it moves to point B. If point B is at #(6 ,3 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
Jul 31, 2017

Answer:

#t = 2.90# #"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((2-6)^2 + (1-3)^2 + (5-7)^2) = 4.90# #"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 #7/6# #"m/s"^2#)

Plugging in known values, we have

#4.90# #"m"# #=0t + 1/2(7/6color(white)(l)"m/s"^2)t^2#

#t = sqrt((4.90color(white)(l)"m")/(7/12color(white)(l)"m/s"^2)) = color(red)(ul(2.90color(white)(l)"s"#