Incorrect o a particle is give0.572-2.31t+ 5.25, where s is in feet and the time
ID: 1878168 • Letter: I
Question
Incorrect o a particle is give0.572-2.31t+ 5.25, where s is in feet and the time t is in seconds. Plot the displacementelcityd oeleration as motion. After you have the plots, answer the questions as a check on your work 2.31t +5.25, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions s, ft -1 01 2 3 Questions: When t-0.8 sec, v-3.206 a -2.42 ft/sec, /sec2 When t 5.2 sec, v -124.22 a- 118.54 t/sec, t/sec The positive time at which the particle changes direction isExplanation / Answer
Given
s(t) = 0.33t^3 - 0.57t^2-2.31t+5.25
we know that the velocity is the differentiation of displacement w.r.t time
v(t) = 0.33*3*t^2 - 0.57*2t-2.31
and
acceleration is
a(t) = 0.33*3*2*t - 0.57*2*1
velocity at t= 1 s to t= 8 s is
v(1) = 0.33*3*1^2 - 0.57*2*1-2.31 = -2.46 m/s
v(2) = 0.33*3*2^2 - 0.57*2*2-2.31 = -0.63 m/s
v(3) = 0.33*3*3^2 - 0.57*2*3-2.31 = 3.18 m/s
v(4) = 0.33*3*4^2 - 0.57*2*4-2.31 = 8.97 m/s
v(5) = 0.33*3*5^2 - 0.57*2*5-2.31 = 16.74 m/s
v(6) = 0.33*3*6^2 - 0.57*2*6-2.31 = 26.49 m/s
v(7) = 0.33*3*7^2 - 0.57*2*7-2.31 = 38.22 m/s
v(8) = 0.33*3*8^2 - 0.57*2*8-2.31 = 51.93 m/s
for acceleration
a(t) = 0.33*3*2*t - 0.57*2*1
a(1) = 0.33*3*2*1 - 0.57*2*1 = 0.84 m/s2
a(2) = 0.33*3*2*2 - 0.57*2*1 = 2.82 m/s2
a(3) = 0.33*3*2*3 - 0.57*2*1 = 4.8 m/s2
a(4) = 0.33*3*2*4 - 0.57*2*1 = 6.78 m/s2
a(5) = 0.33*3*2*5 - 0.57*2*1 = 8.76 m/s2
a(6) = 0.33*3*2*6 - 0.57*2*1 = 10.74 m/s2
a(7) = 0.33*3*2*7 - 0.57*2*1 = 12.72 m/s2
a(8) = 0.33*3*2*8 - 0.57*2*1 = 14.7 m/s2
Now v(0.8) = 0.33*3*0.8^2 - 0.57*2*0.8-2.31 = -2.5884 m/s
a(0.8) = 0.33*3*2*0.8 - 0.57*2*1 m/s2 = 0.444 m/s2
and
v(5.2) = 0.33*3*5.2^2 - 0.57*2*5.2-2.31 =18.5316 m/s
a(0.8) = 0.33*3*2*5.2 - 0.57*2*1 m/s2 = 9.156 m/s2
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v(1) = 0.33*3*1^2 - 0.57*2*1-2.31 = -2.46 m/s
v(2) = 0.33*3*2^2 - 0.57*2*2-2.31 = -0.63 m/s
v(3) = 0.33*3*3^2 - 0.57*2*3-2.31 = 3.18 m/s
from the above dat V(t) values the positive time at which the particle changes direction sis t = 3 s