Show all of your work in thespace provided. Show all of your work to get full credit. Allanswers have to be in SI units(20 pints for eachquestions).

2.Following are the two sets ofposition and time data collected using a motion sensor andcart.

       Table 1. table 2

Time (s)	Position (m)	V(instantaneous) (m/s)
0	10.0
0.25	13.0
0.50	16.5
0.75	21.0
1.00	26.5
1.25	32.3
1.50	38.0
1.75	44.5
2.00	52.0
2.25	60.0
2.50	68.5
2.75	77.5
3.00	87.0
3.25	97.0
3.50	108.0
3.75	119.5
4.00	131.5

Time (s)	Position (m)	V(instantaneous) (m/s)
1	0.972
1.25	1.139
1.5	1.269
1.75	1.362
2	1.416
         2.25	1.432
2.5	1.412
2.75	1.356
3	1.265
3.25	1.139
3.5	0.979

  

1. For Table 1 and Table 2 data plot on graph paper the positionvs time graph and identify the type of motion of the cart on thetrack whether it is on horizontal plane or inclined plane. If thebest fit coefficients (quadratic coefficients) for Table 1 data areA=4.6,    B=11.8,C= 9.8 and for Table 2 data are A=-0.29, B=1.31, C= -0.049 write the corresponding equation of motionconnecting position velocity and acceleration in each cases.Identify the initial position, initial velocity and acceleration inboth cases.(6 point)

      

1. Calculate the instantaneous velocities in both cases(fill intables) and plot the graph of instantaneous velocity vs time forTable 1 and Table 2 data. While calculating the instantaneousvelocity, use time interval of 0.25s.(4 point)
2. Identify the best fit equations in the above cases and comparewith known equation of motion and obtain the values of initialvelocity and acceleration. How these values compare with values inpart A? What is the average velocity in both cases?.(6 point)