a) x = [tex]14t^{2} -2t^{3}[/tex]
at t = 5s
[tex]x = 14*5^{2} -2*5^{3} = 14*25 - 2*125 = 350 - 250 = 100 m[/tex]
b) v = [tex]\frac{dx}{dt}[/tex]
= [tex]28t - 6t^2[/tex]
at t = 5 s
v = [tex]28*5-6*25 = 140 - 150 = -10 m/s[/tex]
c) a = [tex]\frac{dv}{dt}[/tex]
= 28 - 12t
at t = 5 s
a = 28 -12*5= 28-60= -32 m/[tex]s^2[/tex]
d) At maximum positive coordinate velocity = 0
So, [tex]0 = 28t - 6t^2[/tex]
[tex]t = \frac{28}{6} = \frac{14}{3} = 4.66 s[/tex]
At t = 4.66 s
[tex]X = 14 * 4.66^2 - 2* 4.66^3 = 202.39 m[/tex]
e) At t = 4.66 s
f) At maximum positive velocity a = 0
[tex]0=28-12t[/tex]
[tex]t = \frac{28}{12} = \frac{7}{3} = 2.33 s[/tex]
At t = 2.33 s
V = [tex]28*2.33- 6*2.33^2= 32.67 m/s[/tex]
g) t = 2.33 s
h) When particle is not moving v = 0
So [tex]0= 28t - 6 t^2[/tex]
[tex]t = \frac{28}{6} = 4.66 seconds[/tex]
At t = 4.66 s
a = [tex]28 - 12 * 4. 66 = -27.93m/s^2[/tex]
i) At t = 0s, X =0m
t = 5s, X = 100m
So, Displacement = 100m
Velocity = [tex]\frac{Displacement}{Time} = \frac{100}{5} = 20m/s[/tex]
