At the electromagnetics lab, your computer analyzes the track left behind by an

Question

At the electromagnetics lab, your computer analyzes the track left behind by an electron in your lab. The computer analysis reveals that the position of the electron is well approximated by the function r(t)=(t33t26t2+18t)i^ r(t)=(t33t26t2+18t)i^ for the time interval starting at 0 s and ending at 6 s. Note that the time variable in the formula is assumed to be in s and the distance unit is assumed to be a centimeter. 6[W]) What is the rate of change of the acceleration magnitude with respect to time?

Explanation / Answer

The first position vector is

r1(t)=(t33t26t2+18t)i^

Velocity is v1 =dr1/dt =d((t33t26t2+18t)i^/dt =(3t2-6t)im/s

The second position vector after some time interval is

r2(t)=(t33t26t2+18t)i^

The second velocity is v2 =dr2/dt =3t2-6t-12t =(3t2-18t)im/s

The rate of change of the acceleration magnitude with respect to time is given by

a =(3t2-18t)i-(3t2-6t)i/6*10-6s =-12tm/s/6*10-6s =-2t*106m/s2

da/dt =-2*106m/s2

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