A clarinetist, setting out for a performance, grabs his 3.130 kg3.130 kg clarinet case (including the clarinet) from the top of the piano and carries it through the air with an upward force of 29.17 N.29.17 N. Find the case's vertical acceleration. Indicate an upward acceleration as positive and a downward one as negative. Use for g=9.810 m/s2g=9.810 m/s2 for the acceleration due to gravity.

-0.49 m/s²

Explanation:

Given that.

Mass of the clarinet case, m = 3.13 kg

Force acting on the case upwards, F(u) = 29.17 N

Gravitational force acting on the case, F(g)

We will use this very simple equation to understand the relationship between the 3 forces

Applied Force - Gravitational Force = Net Force, or symbolically represented by

F(u) - F(g) = F. If we go ahead to substitute, we have something like

29.17 - (3.13 * 9.81) = F

F = 29.17 - 30.71

F = -1.54 N

This means that the clarinet will accelerate downwards.

Now, Remember also, F = ma. So that

a = F/m

a = -1.54 / 3.13

a = -0.49 m/s²

This thus, is a negative acceleration

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.