Find the work done by a force f = 6i − 8j + 9k that moves an object from the point (0, 10, 4) to the point (4, 16, 18) along a straight line. the distance is measured in meters and the force in newtons.

102 J

Explanation:

Work done by a force

= Force x displacement

In case of vector form of force and displacement , we take dot product of force and displacement to calculate work.

The vector form of line which joins the two given points is given by the equation

d = (4-0) i +(16 - 10)j +( 18 - 4 )k

= 4i +6j +14k

Work done = F . d

(6 i -8J+9k) . ( 4i +6 j + 14 k )

24-48 +126

= 102 J

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 two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.