How close does the plot of velocity vs. time fit a linear regression? (Hint: In

Question

How close does the plot of velocity vs. time fit a linear regression? (Hint: In Capstone, the closer r is to one, the better the fit of data to the curve.)

Did the linear fit of velocity vs. time yield an initial position? If yes, what is the initial position?

Did your linear fit of velocity of velocity vs. time yield an initial speed? If yes, what is the initial speed?

Did your linear fit of velocity vs. time yield an acceleration? If yes, what is the acceleration?

Is the acceleration in the acceleration vs. time graph constant? (Remember, a nearly horizontal line of fit (near zero slope) indicates a constant value.)

Did the linear fit of acceleration vs. time yield an initial speed? If yes, what is the initial speed?

Why is the acceleration vs. time plot so much “noisier” than the other plots?

POSITION VS TIME VALUE Linear Fit m 0.332 b 0.0928 y=mx+b y=(0.332)t+(0.0928) Quadratic Fit A 0.147 B 0.0379 C 0.193 y=Ax2+Bx+C y=(0.147)t2 +(0.0193)t +(0.193) (x1,y1) (1, 0.378m) (x2,y2) (0.950, 0.362) Slope 0.32 m/s VELOSITY VS TIME VALUE m 0.292 b 0.0381 y=mx+b y=(0.292)t + (0.0381) (x1,y1) (1, 0.33) (x2,y2) (0.950, 0.32) Vaverage 0.33 Vaverage time 1.00 seconds ACCELERATION VS TIME VALUE m 0.0110 b 0.292 y=mx+b y=(0.0110)t + (0.292) The mean 0.303

Explanation / Answer

Given equations

Positioon vs time graph

For linear fit

y=(0.332)t+(0.0928)

for quadratic fit

y=(0.147)t2 +(0.0193)t +(0.193)

velocity vs time graph

y=(0.292)t + (0.0381)

Acceleration vs time graph

y=(0.0110)t + (0.292)

1. velocity vs time graph cannot tell us about the initial position, the position time graph can

2. linear fit of velocity vs time gave intial speed in the form of y intercept

equation

y=(0.292)t + (0.0381)

so y intercept = initial speed = 0.0381 m/s

3. slope of velocity time graph is acceleration

equaiton

y=(0.292)t + (0.0381)

so slope = a = 0.292 m/s/s

4. the acceleration in acceleration vs time graph is nearly constant

equation

y=(0.0110)t + (0.292)

slope = 0.0110 (nearly 0)

5. Linear fit of acceleration time graph can never yield ionital velocity

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