Show that if the net force on a particle constrained to move in 1 dimension depends only on position, f-f), the newton's second law can be solved to find v as a function ofx given by: 1 dv2 2 dx v2-si +副0f(x')dx'. note: use the chain rule: dt- = 2dte b) consider a mass constrained to move along x-axis and subject to a net force f =-kx, where k > 0 is a constant. the mass is released form rest at x xo at t-0. use the equation for velocity from part a) to find (x) = . separate the variables and integrate to obtain the time dependence of the position of this mass. hint: when solving the awkward integral you will obtain, use first the suband then ucos 0 in subsequent integral. dt dx dt dx

this means that the temperature of both substances will be equal

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.

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min