Explanation:
It is given that,
A particle starts from rest and has an acceleration function as :
[tex]a(t)=(5-10t)\ m/s^2[/tex]
(a) Since, [tex]a=\dfrac{dv}{dt}[/tex]
v = velocity
[tex]dv=a.dt[/tex]
[tex]v=\int(a.dt)[/tex]
[tex]v=\int(5-10t)(dt)[/tex]
[tex]v=5t-\dfrac{10t^2}{2}=5t-5t^2[/tex]
(b) [tex]v=\dfrac{dx}{dt}[/tex]
x = position
[tex]x=\int v.dt[/tex]
[tex]x=\int (5t-5t^2)dt[/tex]
[tex]x=\dfrac{5}{2}t^2-\dfrac{5}{3}t^3[/tex]
(c) Velocity function is given by :
[tex]v=5t-5t^2[/tex]
[tex]5t-5t^2=0[/tex]
t = 1 seconds
So, at t = 1 second the velocity of the particle is zero.
