(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose the positon vector for a particle is given as a function of time by vector r(t)

=x(t)i + y(t)j with x(t) =at + b and y(t) = ct2 + d, where a=1.00 m/s, b=1.00m,

c=.125 m/s2, and d=1.00m. (a) Calculate the average velocity from t=2.00s to t=4.00s.

(b) Determine the velocity and the speed at t=2.00s

2. Relevant equations

(a) plug in the values for a, b, c, and d to

x(t) = at + b and y(t) = ct2 + d

Vavg = delta r / delta t

3. The attempt at a solution[/c]

(a) Ri =

x(t) = (1.00m/s) 2.00s + 1.00m = 3.00 m/s

y(t) = (.125m/s2) 2.00s2 + 1.00m = 2.41 m/s

Rf

x(t) = (1.00m/s) 4.00s + 1.00m = 5m/s

y(t) = (.125m/s) 4.00s2 + 1.00m = 6.66m/s

Rf -Ri / Tf - Ti

Rf = 6.66 - 2.41 = 4.25

Ri = 5 - 3 = 2

t = 2

4.25 - 2 /2 = 1.13 Vavg from t = 2 to t=4

(b) From equation at 2 s

velocity is

x(t) = 2.41

y(t) = 3

velocity is 5.41 m/s at t=2

Speed is magnitute of vector square root of (3)2 + (2.41)2 = square root of 14.81

Speed = 3.85 m/s

Am I right or close?

Thanks for the help

Kevin

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# Homework Help: Two Dimension Motion Vectors

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