Question

A particle is in motion and is accelerating. The functional form of the velocity is v(t) = 20t − 5t2 m/s . f. Interpret the results of (c) in terms of the directions of the acceleration and velocity vectors. (c. Find Position of the particle at 1, 2, 3, and 5 s. S(1)=10(1)2- (5(1)3)/3= 8.33m S(2)=10(2)2- (5(2)3)/3= 26.67m S(3)=10(3)2- (5(3)3)/3= 45m S(5)=10(5)2- (5(5)3)/3= 41.67m

          A particle is in motion and is accelerating. The functional form
of the velocity is v(t) = 20t − 5t2 m/s .
f. Interpret the results of (c) in terms of the directions of
the acceleration and velocity vectors.
(c. Find Position of the particle at 1, 2, 3, and 5 s.
S(1)=10(1)2- (5(1)3)/3= 8.33m
S(2)=10(2)2- (5(2)3)/3= 26.67m
S(3)=10(3)2- (5(3)3)/3= 45m
S(5)=10(5)2- (5(5)3)/3= 41.67m
        
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Added by David N.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A particle is in motion and is accelerating. The functional form of the velocity is v(t) = 20t − 5t2 m/s . f. Interpret the results of (c) in terms of the directions of the acceleration and velocity vectors. (c. Find Position of the particle at 1, 2, 3, and 5 s. S(1)=10(1)2- (5(1)3)/3= 8.33m S(2)=10(2)2- (5(2)3)/3= 26.67m S(3)=10(3)2- (5(3)3)/3= 45m S(5)=10(5)2- (5(5)3)/3= 41.67m
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Transcript

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00:01 In this question, we have given that a particle is in motion and the particle is accelerating.
00:08 And we have given the velocity with respect to time that is equal to 20 t minus 5 t square.
00:17 And we have given the acceleration with respect to time that is equal to 20 minus 10 t.
00:27 T.
00:28 So we need to find the position of the particle at one second, two second, three second and the five second.
00:38 So we know that the velocity is equal to dx with respect to dt.
00:45 From here, if we calculate our dx, so dx will be equal to v multiply by dt, and if we integrate both side, so what we will get that x, will be equal to integration of 20 t minus 5 t squared multiplied by d t so x will be equal to nothing but 10 t square minus 5 t cube divided by 3 only this is the this is the value of x with respect to time right now we need to find the position at different time interval so in the case when when t is equal to one second so x will be equal to 10 minus 5 divided by 3 so x will be equal to 25 divided by 3 meter 25 divided by 3 meter in the second case we have time is equal to 2 second so x will be equal to 10 multiplied by 2 square that will be 4 only minus 5 multiplied by 2 cube will be 8 divided by 3...
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