Answer:
The equation that describes the motion of the object is [tex]s(t)=20t^2-20t+10[/tex]
Step-by-step explanation:
It is given that,
Acceleration of the object at time t is:
[tex]a(t)=40\ ft/s^2[/tex]
Initial velocity or velocity at t = 0, [tex]v(0)=-20\ ft/s[/tex]
Initial position or position at t = 0, [tex]s(0)=10\ ft[/tex]
Since, [tex]v(t)=\int\limits {a(t).dt}[/tex]
[tex]v(t)=\int\limits {40.dt}[/tex]
[tex]v(t)=40t+c_1[/tex]............(1)
At t = 0, [tex]v(0)=-20\ ft/s[/tex]
→ [tex]c_1=-20[/tex]
Equation (1) becomes :
[tex]v(t)=40t-20[/tex]
Since, [tex]s(t)=\int\limits {v(t).dt}[/tex]
[tex]s(t)=\int\limits {(40t-20).dt}[/tex]
[tex]s(t)=\dfrac{40t^2}{2}-20t+c_2[/tex]............(2)
At t = 0, [tex]s(0)=10\ ft/s[/tex]
→ [tex]c_1=10[/tex]
Equation (2) becomes:
[tex]s(t)=20t^2-20t+10[/tex]
Hence, this is the required solution.
