An object is at rest at #(7 ,9 ,4 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(5 ,1 ,8 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
1 Answer
Jun 13, 2017
Explanation:
We're asked to find the time
We can use the equation
where
#Deltax# is the change in position of the object, which is simply the distance between the two coordinate points:
#Deltax = sqrt((5"m"  7"m")^2 + (1"m"  9"m")^2 + (8"m"  4"m")^2)#
#= 9.17# #"m"#

#v_(0x)# is the initial velocity, which is#0# since it started from rest, 
#t# is the time, which is what we're trying to find, and 
#a_x# is the acceleration, which is#7/4# #"m/s"^2# .
Plugging in known variables we have
The object will travel the distance in