Question

Let s(t) denote the position of a particle at time t, and let v and a be the velocity and acceleration respectively. The particle is moving according to the data v(t)=sin(t)−cos(t),s(0)=−10. Find a function describing the position of the particle.

Answer 1

Answer:

s(t) = -cos(t) -sin(t) -9

Step-by-step explanation:

The velocity (v) of a moving particle is the rate of change of poisition (s)  i.e

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

from the above equation s becomes:

$s=\int\(v(t)} \, dt$

from the given data

$v(t) = sin(t) - cos(t)$

therefore,$s(t) = \int\ {sin(t)- cos(t)} \, dt\\ s(t) = \int\ sin(t) dt - \int\ cos(t) dt\\\\s(t) = -cos(t) - sin(t) +C\\put \\t=0\\s(0) = -cos(0) - sin(0) +C\\-10 = -1 -0 +C\\C = -10+1\\C=-9\\therfore,\\s(t) = -cos(t) -sin(t) -9$