F = force (N)x = distance (m)m = mass (kg)V = velocity (m/s)t = time (s)Which one of the following equations is dimensionally homogeneous? (Select all that apply.)F(x2 − x1) = 12mV22 − 12mV12F = 12mV22 − 12mV12F(V2 − V1) = 12mx22 − 12mx12F(t2 − t1) = mV2 − mV1

The concept of dimensional homogeneity states that every term in an equation must have the same dimension. This means that the units on both sides of the equation must be the same.

Let's check each equation:

1. F(x2 − x1) = 1/2mV22 − 1/2mV12 The left side of the equation has units of force times distance (Nm), while the right side has units of energy (kgm^2/s^2). These are not the same, so this equation is not dimensionally homogeneous.

2. F = 1/2mV22 − 1/2mV12 The left side of the equation has units of force (N), while the right side has units of energy (kg*m^2/s^2). These are not the same, so this equation is not dimensionally homogeneous.

3. F(V2 − V1) = 1/2mx22 − 1/2mx12 The left side of the equation has units of force times velocity (Nm/s), while the right side has units of energy (kgm^2/s^2). These are not the same, so this equation is not dimensionally homogeneous.

4. F(t2 − t1) = mV2 − mV1 The left side of the equation has units of force times time (Ns), while the right side has units of momentum (kgm/s). These are not the same, so this equation is not dimensionally homogeneous.

Therefore, none of the given equations are dimensionally homogeneous.

The concept of dimensional homogeneity states that every term in an equation must have the same dimension. This means that the units on both sides of the equation must be the same.

Let's check each equation:

1. F(x2 − x1) = 1/2mV22 − 1/2mV12 The left side of the equation has units of force times distance (Nm), while the right side has units of mass times velocity squared (kg(m/s)^2). These are not the same, so this equation is not dimensionally homogeneous.

2. F = 1/2mV22 − 1/2mV12 The left side of the equation has units of force (N), while the right side has units of mass times velocity squared (kg*(m/s)^2). These are not the same, so this equation is not dimensionally homogeneous.

3. F(V2 − V1) = 1/2mx22 − 1/2mx12 The left side of the equation has units of force times velocity (N*(m/s)), while the right side has units of mass times distance squared (kg*m^2). These are not the same, so this equation is not dimensionally homogeneous.

4. F(t2 − t1) = mV2 − mV1 The left side of the equation has units of force times time (Ns), while the right side has units of mass times velocity (kg(m/s)). These are not the same, so this equation is not dimensionally homogeneous.

Therefore, none of the given equations are dimensionally homogeneous.