2. Of Calculus and Plotting:2 A particle moves along the r-axis according to: 2(

Question

2. Of Calculus and Plotting:2 A particle moves along the r-axis according to: 2(t) = (10 ms-1)t-(2 ms-2)t2. Note: since position, velocity, and acceleration are all vectors, in full-blown physics glory this should bet) = ((10 m s-yt-(2 ms-2)H) i. but we will not require vector notation for this problem. We should just remember's 1D, where positive r(t), v(t), and a(t) refer to the positive r-direction (ie.. + (a) Derive the equation for instantaneous velocity u(t) and compute u(2 s and u(39 (b) Compute the average velocity between 2s and 3s two different ways. (c) Derive the equation for instantaneous acceleration a(t) (d) Accurately graph x(t), u(t), and a(t) from t =-1 s to t = 6 s on the same plot. Include the clearly labeled figure with your homework submission. (It is recommended you use a spreadsheet like Google Sheets, Microsoft Excel, or Apple Numbers. Please ask for help; spreadsheet skillz are useful.)

Explanation / Answer

x(t) = 10t - 2t2

a] v = dx/dt

so, differentiate the above expression to find instantaneous velocity

=> v(t) = 10 - 4t

at t = 2s, v(2) = 10 - 4(2) = 2 m/s

and at t = 3s, v(3) = 10 - 4(3) = - 2 m/s.

b] average velocity = [v2 - v1]/[t2 - t1]

so, vavr = [- 2 -2]/[3-2] = - 4 m/s

and using the statistical average, vavr = (-2+2)/2 = 0 m/s

c] a(t) = dv/dt

so, differentiate the expression for v(t) to get instantaneous acceleration

a(t) = 0 - 4 = - 4 m/s2.

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