![]() ![]() We can plug this in for the attraction force, giving us this:Ĭanceling out m2, we get a definition for gravitational acceleration:įrom here, we have to use measurements to help us. So, the mass on the left side of the following equation would refer to the person, which we can arbitrarily call m2. Here, we are looking for the force on the person from the earth. If we take this equation and frame it in terms of somebody standing on the earth, we get a force due to gravitational attraction that is the product of their masses divided by the square of the earth's radius.įrom here, we can take Newton's second law of motion, f = ma. If you look at Newton's law of universal gravitation, you see that the force of attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. ![]() A heavier object has more inertia, which is a resistance to a change in motion. While it's true that there is more gravitational force acting on a heavier object, this doesn't correspond to an increase in acceleration. In order to make this equation more universal, the position equation can be generalized as x(t) = 1/2(at^2) + v_0 + x_0 Simplifying the integral results in the position equation x(t) = -4.9t^2 + (C_1)t + C_2, where C_1 is the initial velocity and C_2 is the initial position (in physics, C_2 is usually represented by x_0). Position is the antiderivative of velocity, so that means that x'(t) = v(t) and x(t) = int. To find the position equation, simply repeat this step with velocity. This means that for every second, the velocity decreases by -9.8 m/s. Simplifying the integral results in the equation v(t) = -9.8t + C_1, where C_1 is the initial velocity (in physics, this the initial velocity is v_0). We can use this knowledge (and our knowledge of integrals) to derive the kinematics equations.įirst, we need to establish that acceleration is represented by the equation a(t) = -9.8.īecause velocity is the antiderivative of acceleration, that means that v'(t) = a(t) and v(t) = int. We know that acceleration is approximately -9.8 m/s^2 (we're just going to use -9.8 so the math is easier) and we know that acceleration is the derivative of velocity, which is the derivative of position. The goal of this first unit of The Physics Classroom has been to investigate the variety of means by which the motion of objects can be described.We usually start with acceleration to derive the kinematic equations. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations ( position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. ![]() There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s 2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. ![]() However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s 2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop and you do not know the time required to skid to a stop. ![]()
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