Hi all, Im having a bit of troublesolving the following problem. I can solve for

Question

Hi all, Im having a bit of troublesolving the following problem. I can solve for Particle B byusing standard metric unit formulae (solving for distance andvelocity), but I cant solve for Particles A and C, as the formulaecontinue to have too many variables. I also am not sure of howto plot a graph that will show all relevant values derived asa funtion of time. How can this be done?
Particle A is subject to an acceleration ofa = -0.5v (m/s2),particle B is subject to an accelerationof a = -1.0t(m/s2), and particle C issubject to an acceleration of a= -0.5s (m/s2). All three particlesstart at the origin s= 0 m, and with an initialvelocity of v0= 20 m/s.Derive expressions for position, velocity and acceleration as afunction of time, and plot the magnitude of these three values forthe time interval from 0 to 5 seconds. Use the same axes for allthree plots of each variable so that a decent comparison can bemade (e.g. plot position of A, B and C on one graph), etc. Nowrepeat these plots for the time interval from 0 to 20 seconds andcomment on your answers. Any help would begreatly appreciated. -nick. Hi all, Im having a bit of troublesolving the following problem. I can solve for Particle B byusing standard metric unit formulae (solving for distance andvelocity), but I cant solve for Particles A and C, as the formulaecontinue to have too many variables. I also am not sure of howto plot a graph that will show all relevant values derived asa funtion of time. How can this be done?
Particle A is subject to an acceleration ofa = -0.5v (m/s2),particle B is subject to an accelerationof a = -1.0t(m/s2), and particle C issubject to an acceleration of a= -0.5s (m/s2). All three particlesstart at the origin s= 0 m, and with an initialvelocity of v0= 20 m/s.Derive expressions for position, velocity and acceleration as afunction of time, and plot the magnitude of these three values forthe time interval from 0 to 5 seconds. Use the same axes for allthree plots of each variable so that a decent comparison can bemade (e.g. plot position of A, B and C on one graph), etc. Nowrepeat these plots for the time interval from 0 to 20 seconds andcomment on your answers. Any help would begreatly appreciated. -nick.

Explanation / Answer

The expressions for position are S1 = vot +(1/2)a1t2 S2 = vot +(1/2)a2t2 and S3 = vot +(1/2)a3t2 vo = 20 m/s,a1 = -0.5vom/s2,a2 = -1.0t m/s2 anda3 = -0.5s m/s2 substituting the values in the above equation we get S1 = 20t + (1/2) * -0.5vo *t2 = 20t - 0.25 * 20 * t2 = 20t -5t2 S2 = 20t + (1/2) * -1.0t * t2 =20t - 0.5t3 and S3 = 20t + (1/2) * -0.5S3 = 20t -0.25S3 or (1 + 0.25) * S3 = 20t or S3 = (20t/1.25) = 16t the values of S1,S2 and S3for the time interval from 0 to 5 seconds are S1 = 20 * 0 - 5 * 02 = 0,S1 =20 * 1 - 5 * 12 = 15 m,S1 = 20 * 2 - 5 *22 = 20 m,S1 = 20 * 3 - 5 * 32 =15 m, S1 = 20 * 4 - 5 * 42 = 0 m andS1 = 20 * 5 - 5 * 52 = -25 m S2 = 20 * 0 - 0.5 * 03 = 0,S2= 20 * 1 - 0.5 * 13 = 19.5 m,S2 = 20 * 2- 0.5 * 23 = 36 m, S2 = 20 * 3 - 0.5 * 33 = 46.5m,S2 = 20 * 4 - 0.5 * 43 = 48m,S2 = 20 * 5 - 0.5 * 53 = 37.5 m S3 = 16 * 0 = 0,S3 = 16 * 1 = 16m,S3 = 16 * 2 = 32 m,S3 = 16 * 3 =48 m,S3 = 16 * 4 = 64 m and S3 = 16 * 5 = 80 m We can plot the S1 versus t,S2 versus tand S3 versus t by taking S on y-axis and t onx-axis or (1 + 0.25) * S3 = 20t or S3 = (20t/1.25) = 16t the values of S1,S2 and S3for the time interval from 0 to 5 seconds are S1 = 20 * 0 - 5 * 02 = 0,S1 =20 * 1 - 5 * 12 = 15 m,S1 = 20 * 2 - 5 *22 = 20 m,S1 = 20 * 3 - 5 * 32 =15 m, S1 = 20 * 4 - 5 * 42 = 0 m andS1 = 20 * 5 - 5 * 52 = -25 m S2 = 20 * 0 - 0.5 * 03 = 0,S2= 20 * 1 - 0.5 * 13 = 19.5 m,S2 = 20 * 2- 0.5 * 23 = 36 m, S2 = 20 * 3 - 0.5 * 33 = 46.5m,S2 = 20 * 4 - 0.5 * 43 = 48m,S2 = 20 * 5 - 0.5 * 53 = 37.5 m S3 = 16 * 0 = 0,S3 = 16 * 1 = 16m,S3 = 16 * 2 = 32 m,S3 = 16 * 3 =48 m,S3 = 16 * 4 = 64 m and S3 = 16 * 5 = 80 m We can plot the S1 versus t,S2 versus tand S3 versus t by taking S on y-axis and t onx-axis

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