The location of some particle is given by its x, y, and z coordinates as functio
ID: 2167914 • Letter: T
Question
The location of some particle is given by its x, y, and z coordinates as functions of time as shown:x = 7 m - 3 m/s t - 2 m/s2 t2
y = 10 m - 9 m/s t + 0.05 m/s3 t3
z = - 6 m - 10 m/s t
What is the magnitude of the particle's displacement from 7.79 seconds to 13.51 seconds?
What is the magnitude of the particle's average velocity between 7.79 seconds and 13.51 seconds?
What is the instantaneous speed of the particle at 13.51 seconds?
What is the magnitude of the particle's instantaneous acceleration at 7.79 seconds?
Explanation / Answer
instantaneous speed =sqrt( (dx/dt)^+ (dy/dt)^2 + (dz/dt)^2 ) dx/dt = -3-4t = -57.04 dy/dt = -9+0.15t^2 =18.378 dz/dt = -10 instantenous speed = 60.756 m/s acceleration = sqrt( (d^2x/dt^2)^+ (d^2y/dt^2)^2 + (d^2z/dt^2)^2 ) d^2x/dt^2 = -4 d^2y/dt^2 =0.3t =2.337 d^2z/dt^2=0 acceleration = 4.632 m/s^2 average velocity = magnitude of particles displacement from 7.79 s to 13.51 sec / (13.51-7.79) = 271.34/5.72 = 47.437 m/s magnitude of displacement change in x = -260.832=a change in y = 48.175 8=b change in z = -57.2=c magnitude of displacement = sqrt(a^2+b^2+c^2) =271.34 m
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