# The velocity function (in meters per second) for a particle moving along a line is given byv(t) 3t 7, 0 < t < 3.(a) Find the displacement (in meters) of the particle.Displacement =meters(b) Find the total distance traveled (in meters) by the particle.Total distance traveled =meters

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16 views help_outlineImage TranscriptioncloseThe velocity function (in meters per second) for a particle moving along a line is given by v(t) 3t 7, 0 < t < 3. (a) Find the displacement (in meters) of the particle. Displacement = meters (b) Find the total distance traveled (in meters) by the particle. Total distance traveled = meters fullscreen
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Step 1 help_outlineImage TranscriptioncloseTo determine the following part of the velocity v(t)-3t-7 for the given interval a). displacement of the particle b). total distance traveled by the particle Given information v(t) 3t 7, 0 t<3. Used formula: Integration formula (1) n+1 fullscreen
Step 2 help_outlineImage Transcriptionclosecalculation: for part(a) Displacement of the particle is given below (t)3t-7 v()dt=£(3-7)df (from equation 1) 3 - 7t 2 -70-70 27 = -21 2 27-42 2 15 2 15 meter 2 displacement is fullscreen
Step 3 help_outlineImage Transcriptionclosecalculation for part(b) for total distance of the particle find the interval where the velocity is negative and the interval where the velocity is positive v(t) 3t7 3t 7 0 7 t =-second 3 fullscreen

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### Calculus 