4. What does the slope of each of the following graphs stand for? (y versus x)
a) mass vs volume
b) velocity vs time
c) mass vs force
d) kinetic energy vs frequency
e) sine incident angle vs sine refracted angle
f) charge vs voltage
g) voltage vs current
h) force vs area
a) density
b) acceleration
c) -
d) -
e) refractive index
f)capacity
g)resistance
h) pressure
Thank you!
To understand what the slope of each graph represents, we need to recall the general formula for slope, which is given by:
slope = (change in y) / (change in x)
a) In the graph of mass vs volume, the slope represents the density of the substance. Density is defined as mass per unit volume. So, the slope of this graph would give us the mass-to-volume ratio or the density.
b) For the velocity vs time graph, the slope is equal to the acceleration of the object. Acceleration is the rate of change of velocity with respect to time. Therefore, the slope of this graph would represent acceleration.
c) In the mass vs force graph, the slope represents the acceleration of the object. According to Newton's second law of motion, force is equal to mass multiplied by acceleration (F = m*a). Therefore, the slope of this graph would give us the value of acceleration.
d) The kinetic energy vs frequency graph doesn't have a specific physical interpretation for the slope, as kinetic energy and frequency are not directly related in a simple way. Therefore, without more context or additional information, it's difficult to assign a meaning to the slope in this case.
e) In the sine incident angle vs sine refracted angle graph, the slope represents the refractive index or the ratio of the speed of light in vacuum to the speed of light in the medium. This is as per Snell's law of refraction which states that the ratio of sines of the incident angle to the refracted angle is equal to the ratio of velocities or index of refraction.
f) In the charge vs voltage graph, the slope represents the capacitance of a system. Capacitance is defined as the ratio of the amount of electric charge stored in a system to the potential difference (voltage) across it. So, the slope of this graph would give us the value of capacitance.
g) The voltage vs current graph represents Ohm's Law in a circuit. The slope of this graph would be equal to the resistance of the circuit. Resistance is defined as the ratio of voltage to current (R = V/I). Therefore, the slope of this graph would provide the value of resistance.
h) In the force vs area graph, the slope represents the pressure acting on the surface. Pressure is defined as the force per unit area. So, the slope of this graph would give us the value of pressure.