The motion of two carts is described with the following equations: x(t) = 7t + 6
ID: 1594699 • Letter: T
Question
The motion of two carts is described with the following equations: x(t) = 7t + 6t2 and x(t) = 31t. Provide as much information as possible about the motion of these two objects. (Assume x is in meters, t is in seconds, and t 0. ) Will these two objects meet? Yes No If yes, when and where? (Enter your answers to at least three significant figures. If no, enter NONE.) x = m t = s Present their motion graphically with a sketch of position vs. time graphs in one coordinate system. The sketch needs to be attached at "Show my work". (Upload a file with your sketch. Either scan your sketch as a file or take a photo. Submit it with a maximum size of 1 MB. Present your sketch to your TA to sign.) Choose File
Explanation / Answer
First cart :
X1(t) = 7t + 6t2
at t = 0 , the cart is at origin , X1(0) = 0
taking derivative both side
V1(t) = 7 + 12t
at t = 0 , V1(0) = 7 m/s
hence the cart starts with velocity 7 m/s
acceleration is given as
a1(0) = 7
hence the cart moves at constant acceleration
second cart :
X2(t) = -31 t
at t = 0 , the cart is at origin , X2(0) = 0
taking derivative both side
V2(t) = - 31
at t = 0 , V2(0) = - 31 m/s
hence the cart starts with velocity - 31 m/s
acceleration is given as
a2(0) = 0
hence the cart moves at constant speed
for The two carts to meet ,
X1(t) = X2(t)
7t + 6t2 = - 31 t
solving the equation , we get t = 0 and imaginary value of time
hence the carts dont meet after starting from origin