An object is at rest at #(3 ,5 ,1 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(9 ,9 ,8 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
1 Answer
Explanation:
We're asked to find the time it takes for the object to move from
To do this, we can use the equation
Our known quantities are
#Deltax# is the change in position of the object from the two coordinate points. We can find the distance between these two coordinates and call this the change in position:
#Deltax = sqrt((9"m"3"m")^2 + (9"m"5"m")^2 + (8"m"1"m")^2)#
#= color(red)(10.0"m"#

#v_(0x)# is the initial velocity of the object. Since it's originally at rest, this value is zero. 
#a_x# is the object's (constant) acceleration, which is#4/3"m"/("s"^2)#
Plugging in our known values, we have
The object will travel the distance from