The acceleration is the derivative of the velocity.

The acceleration is the derivative of the velocity.

• A. True
• B. False
• C. It equals the velocity
• D. It equals the position

Answer: (A)

Acceleration is the rate at which velocity changes with respect to time, so it is the derivative of velocity. In symbols, a(t) = dv/dt, and this is also the second derivative of position, since v = dx/dt and a = dv/dt = d^2x/dt^2. If velocity stays constant, dv/dt is zero, so acceleration is zero; if velocity grows, acceleration is positive; if velocity shrinks, acceleration is negative. This makes sense because acceleration measures how quickly the speed or direction is changing, not the current value of velocity itself or the position.

Acceleration is the rate at which velocity changes with respect to time, so it is the derivative of velocity. In symbols, a(t) = dv/dt, and this is also the second derivative of position, since v = dx/dt and a = dv/dt = d^2x/dt^2. If velocity stays constant, dv/dt is zero, so acceleration is zero; if velocity grows, acceleration is positive; if velocity shrinks, acceleration is negative. This makes sense because acceleration measures how quickly the speed or direction is changing, not the current value of velocity itself or the position.