a motorcycle traveling on the highway at a velocity of 120 kilometre-per-hour passes a car traveling at a velocity of 90 kilometre-per-hour from the point of view of a passenger on the car what is the velocity of a motorcycle

The relative velocity of the motorcycle to a passenger in the car is 30 km/h

Explanation:

The question relates to the principle of relative velocity and reference frames

The given parameters are;

The velocity of the motorcycle, v₁ = 120 km/h

The velocity of the car, v₂ = 90 km/h

The relative velocity of an object X with regards to another object Y is the velocity the object X will seem to be moving with to an observer in the rest frame of object Y written as = -

Therefore, the relative velocity of the motorcycle to the car is = v₁ -  v₂, which give;

 = 120 km/h - 90 km/h = 30 km/h

The relative velocity of the motorcycle to a passenger in the car = 30 km/h.

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.