Answer:
The displacement of the particle is 78 meters
Explanation:
The velocity function is given for a particle moving along a line is given by ;
[tex]v(t)=t^2-2t-24,\ 1 \le t\le 7[/tex]
We need to find the displacement of the particle. It is equal to s. So,
[tex]\dfrac{ds}{dt}=v[/tex]
[tex]\dfrac{ds}{dt}=t^2-2t-24[/tex]
[tex]s=\int(t^2-2t-24)\ dt[/tex]
[tex]s=\dfrac{t^3}{3}-t^2-24t|_1^7[/tex]
[tex]s=\dfrac{7^3}{3}-7^2-24(7)-(\dfrac{1^3}{3}-1^2-24(1))[/tex]
s = -78 meters
So, the displacement of the particle is 78 meters. Hence, this is the required solution.
