the value of k and the velocity of the particle when x=-2m?
the acceleration of a particle is defined by the relation a=k(1-e^-x), where k is a constant. knowing that the velocity of the particle is v=9m/s when x=-3m and that the particle comes to rest at the origin, determine
- Agent 47Lv 41 decade agoFavorite Answer
a = k(1-e^-x)
Since acceleration is the derivative of velocity, therefore we can write it as
dV/dt = k(1-e^-x)
dV = k(1-e^-x)dt
integral dV = integral [k(1-e^-x)]dt
V = k ( x - (-x) e^-x)
V = k x (1 + e^-x)
when x = -3, v = 9. Put the respective values in above equation.
9 = k (-3) ( 1 + e^-3)
k = -3 / (1 + e^-3)
Solving it, we get
k = -2.8577223806977896287661130596212