#Freefall position and velocity graphs plus#

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.

We usually start with acceleration to derive the kinematic equations.

#Freefall position and velocity graphs plus#

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