One common application of conservation of energy in mechanics is to determine the speed of an object. although the simulation doesn’t give the skater's speed, you can calculate it because the skater's kinetic energy is known at any location on the track. consider again the case where the skater starts 7 m above the ground and skates down the track. what is the skater's speed when the skater is at the bottom of the track?

v=11.71 m/s

Explanation:

Given

Skater is at a height of 7 m above the ground and skate down the track

Conserving Energy At top and Bottom point

Potential Energy converted to Kinetic Energy

Potential Energy

Kinetic Energy

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.

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.