The motion of two carts is described with the following equations: x(t) = 7t + 6

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

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