Calculus Ch 3 Particle Motion

Front

What is the position function for a falling object under gravity?

Back

s(t) = -4.9t² + vt₀ + s₀, where v₀ is the initial velocity and s₀ is the initial position.

Front

How do you find the maximum height of a projectile?

Back

Use the vertex formula t = -b/(2a) for the quadratic equation s(t) = at² + bt + c.

Front

What does a velocity-time graph represent?

Back

It shows the object's velocity over time, indicating acceleration and deceleration.

Front

What does it mean if velocity is negative and acceleration is positive?

Back

The object is slowing down.

Front

How do you determine the initial position from a position function?

Back

Evaluate the position function at t=0.

Front

What is the relationship between position, velocity, and acceleration?

Back

Velocity is the derivative of position, and acceleration is the derivative of velocity.

Front

What is the formula for velocity in terms of position?

Back

v(t) = ds/dt, where s is the position function.

Front

How do you calculate the velocity from a position function x(t)?

Back

Differentiate the position function: v(t) = dx/dt.

Front

What does it mean for an object to be moving with constant velocity?

Back

The object's speed and direction remain unchanged over time.

Front

What is the significance of the second derivative in motion?

Back

The second derivative indicates acceleration, showing how velocity changes over time.