The only force acting on a 2.0 kg body as it moves along a positive x axis has an x component fx = −6 x n, with x in meters. the velocity at x = 3.0 m is 8.0 m/s. (a) what is the velocity of the body at x = 4.0 m? (b) at what positive value of x will the body have a velocity of 5.0 m/s?

a-0

b-2 m

Explanation:

Given mass of the body is 2 kg

Force acting on the body =-6x N

Velocity at x=3m is 8m/s

Now acceleration of the body is -3x

a=-3x

=-3x

vdv=-3xdx

integrating both sides we get

=+c

Now at x=3m v=8m/s

substituting values

c=

Thus

Velocity will be zero after

thus velocity of the body is zero at x=4 m

v=5m/s

25=-3x^2+37

x=2 m

pe = weightxheight = 2000x1000=2,000,000joules

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.