Question

1. <Problem Due> A particle is traveling along the path defined by y=(x - 1)?. If x = 0.562 m, where t is in seconds, calculate the magnitudes of the particle's velocity ū and acceleration ā when t = 1 s. Also, sketch your results and show the directions of ū and ā when t= 1 s.

Answer 1

Title - Velocity & Acceleration Analysis

Solution: Given y = (x-1) a=0.542 m at t=1 To find i v, of displacement Procedure i we know, taking derivative wirrt to time gives velocity - y = (x-17² y = (0.5 2²-1² wwwwww dy , d 0.25 +*-1) 1. www dt 1. j = dy0.25(4.+) dt - ū = dy . 0.25 (4 x (1)) - (at t-i) . dt Mindes mer

Now, relocity wirt As we know, taking derivative of time gives acceleration, sed (0-25(++)) dü. d ( (2).+) dt dit dv. 1. (3.4%) dt .:ās dū - 1.(3 (1)) ... (at t=1) 1. dt m/s2 ā= di = 3 at L Velocity at tuis Acceleration at t=1s ā= 3 m/s² ū= 1 m/s

Conclusion - Velocity is the first derivative of displacement with respect to time while acceleration is the second derivative and the first derivative of velocity with respect to time.

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