1. The force (in Newtons) applied to an object varies jointly as its mass and acceleration. How much force is needed to accelerate a 25 kg object by 3 m/s^2?

1. F = m*a = 25 * 3 = 75 N.

1. Well, let's do some "force-ful" math here! The force is equal to the mass multiplied by the acceleration. So, for a 25 kg object accelerated by 3 m/s^2, the force needed would be enough to make any clown's wig fly off—75 Newtons!

2. Ah, potential energy, the energy of possibilities! To find the constant of variation, we need to divide the potential energy by the product of the mass and height. So, if the potential energy is 30 J and the mass is 1.5 kg at a height of 2 m, our constant of variation is a whopping 10 J/(kg*m). Now, isn't that just "height-lessly" awesome?

1. To find the force needed to accelerate a 25 kg object by 3 m/s^2, you can use the formula for joint variation:

Force = k * mass * acceleration

Here, k represents the constant of variation. Plugging in the given values, we have:

Force = k * 25 kg * 3 m/s^2

Since we need to solve for the force, we can rearrange the equation:

Force = k * 25 kg * 3 m/s^2
Force = (k * 25 * 3) kg * m/s^2
Force = 75k kg * m/s^2

Therefore, the force needed to accelerate a 25 kg object by 3 m/s^2 is 75k newtons.

2. To find the constant of variation for potential energy, we use the formula for joint variation:

Potential Energy = k * mass * height

Given that the potential energy is 30 J, the mass is 1.5 kg, and the height is 2 m, we can plug in these values:

30 J = k * 1.5 kg * 2 m

To solve for k, we can rearrange the equation:

30 J = k * 1.5 kg * 2 m
30 J = (k * 1.5 * 2) kg * m
30 J = 3k kg * m

Therefore, the value of the constant of variation is 3 J/(kg * m).

1. To solve this problem, we need to use the concept of joint variation. Joint variation refers to a relationship where a variable varies directly with two or more other variables, in this case, the force varies jointly with the mass and acceleration.

The formula for joint variation is given as:

f = k * m * a

Here, f represents the force, m represents the mass, a represents acceleration, and k is the constant of variation.

To find the value of the constant of variation, we need to rearrange the formula:

k = f / (m * a)

Now, we can substitute the given values into the formula and solve for the force:

k = f / (25 kg * 3 m/s^2)

2. To solve this problem, we need to use the concept of joint variation. Joint variation refers to a relationship where a variable varies directly with two or more other variables, in this case, the potential energy varies jointly with the mass and height from the ground.

The formula for joint variation is given as:

PE = k * m * h

Here, PE represents the potential energy, m represents the mass, h represents the height, and k is the constant of variation.

To find the value of the constant of variation, we can rearrange the formula:

k = PE / (m * h)

Now, we can substitute the given values into the formula and solve for the constant of variation:

k = 30 J / (1.5 kg * 2 m)