How to integrate with position, velocity and accelleration
The integral of acceleration is velocity.
The integral of velcotiy is position.
All three are vectors, so the integration has to be peformed in three different perpendicular dimensions, in general.
Unless you have a specific example in mind, there is not much more I can say.
well i have this homework question that says:
A rock is dropped from the top of a 300-ft cliff. It's velocity at time t seconds is v(t0= -32 t feet per second.
a.) Find the height of the rock above the ground at time t.
b.) How long will the rock take to reach the ground?
c.) What will be the velocity when it hits the ground?
That is the problem I am working with tonight.
To integrate position, velocity, and acceleration, you can use calculus. Integration allows you to find position given velocity, and velocity given acceleration. Here's how to integrate each of these quantities:
1. Integrating acceleration to find velocity:
- Start with the equation: a(t) = dv(t)/dt, where a(t) represents acceleration, v(t) represents velocity at time t, and dt represents a differential time interval.
- To find velocity, v(t), you need to integrate acceleration, a(t), with respect to time. This can be done by applying the integral sign (∫) on both sides: ∫a(t) dt = ∫dv(t).
- Integrate both sides of the equation, resulting in: v(t) = ∫a(t) dt + C, where C is the constant of integration.
- The integral of acceleration will give you the change in velocity over time, and the constant of integration accounts for the initial velocity.
2. Integrating velocity to find position:
- Start with the equation: v(t) = dx(t)/dt, where v(t) represents velocity, x(t) represents position at time t, and dt again represents a differential time interval.
- To find position, x(t), you need to integrate velocity, v(t), with respect to time: ∫v(t) dt = ∫dx(t).
- Integrate both sides of the equation, resulting in: x(t) = ∫v(t) dt + C, where C is the constant of integration.
- The integral of velocity will give you the change in position over time, and the constant of integration accounts for the initial position.
So, to integrate from acceleration to position, you'll need to integrate acceleration twice: first to find velocity, and then to find position. Remember to include the appropriate constants of integration to account for the initial conditions.