AP Calculus AB and BC glossary

Speed

Speed is the absolute value of velocity, so it is never negative and carries no direction information. Speed increases exactly when velocity and acceleration have the same sign.

speed=∣v(t)∣\text{speed} = |v(t)|

Because speed strips the sign, a particle moving in the negative direction can still be speeding up. Questions that ask whether speed is increasing are really asking you to compare two signs.

For a particle moving along a curve described parametrically, speed is the magnitude of the velocity vector, (dxdt)2+(dydt)2\sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2}.

Appears in: Unit 4: Contextual Applications, Unit 8: Applications of Integration