CAPM Final Challenge

Challenge: Predict where your fan cart and other group's fan cart will collide. Your prediction needs to be within 3 centimeters rather than within 10% error. 

With the data recorded, we calculated the average acceleration of the fan cart using the motion sensor to detect the velocity of the cart. This sensor provided us with a velocity versus time graph of the object's motion along with the equation of the graph: y= mx + b or v = at + initial v. The slope of this line is equivalent to the acceleration. We used the data to create a graph and calculated the average acceleration using the formula: a = ΔV/ΔT.

a = (.61 - 0) / (4 - 0) = .1525 m/s²

^{We recorded this data using Cart A and compared the acceleration of Cart A} 

^{to Cart E. We calculated the acceleration of Cart E to be} .0213 m/s²

^{After we had completed this part, compared our results with with another group to calculate the location in which the two carts would collide.} 

Δx = (1/2) * a * (Δt)^2 + V_it

Cart A:

Δx = (1/2) * (.1525) * (4)^{2 + (0)(4) = 1.22 meters}

^{Cart B:}

Δx = (1/2) * (.0213) * (2)^{2 + (0)(4) =  .426 meters}

^{We calculated that the carts would collide at 29 centimeters. When we actually put the carts to the test, we were only 4 centimeters off.} 

Conclusion: In this experiment we used acceleration to calculate where two carts would collide (traveling in a direct path). We plugged the two formulas into a graphing calculator and calculated where they would collide by calculating the point of intersection. Our prediction was pretty close to our actual results, only 4 centimeters off.