Question

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2 − 2t − 24, 1 ≤ t ≤ 7 (a) Find the displacement. g

Answer 1

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 ;

$v(t)=t^2-2t-24,\ 1 \le t\le 7$

We need to find the displacement of the particle. It is equal to s. So,

$\dfrac{ds}{dt}=v$

$\dfrac{ds}{dt}=t^2-2t-24$

$s=\int(t^2-2t-24)\ dt$

$s=\dfrac{t^3}{3}-t^2-24t|_1^7$

$s=\dfrac{7^3}{3}-7^2-24(7)-(\dfrac{1^3}{3}-1^2-24(1))$

s = -78 meters

So, the displacement of the particle is 78 meters. Hence, this is the required solution.