Principles of Technology Motion - Acceleration Principles of Technology

When the dragster in the figure moves to the right from the initial position at ti to the final position at tf, its velocity at tf is greater than its velocity at ti. The faster the velocity of the dragster changes, the less its time of travel will be. The faster its velocity changes, the larger the acceleration will be. Acceleration is the change in velocity per unit time.

Equation: Δv = change in velocity or speed a = acceleration t = time

Acceleration has a magnitude and a direction and is a vector quantity. Units: m/s2 (most common); ft/s2, or km/hr2. When an object’s velocity and acceleration are in the same direction, the object is speeding up. When an object’s velocity remains the same, the acceleration is zero.

When an object’s velocity and acceleration are in opposite directions, the object is slowing down. The acceleration is considered to be negative and is called deceleration. Insert a negative sign with the numerical value for the acceleration in the equation. Constant or uniform acceleration means that the velocity increases or decreases at the same rate throughout the motion. The rate of change in the velocity is always the same.

Variables to consider: xo = initial displacement xf = final displacement vo = initial velocity vf = final velocity a = acceleration t = time Velocity as a function of time:

Displacement as a function of time:

For motion in which a = 0 m/s2 (no change in velocity): Velocity as a function of displacement: For motion in which a = 0 m/s2 (no change in velocity): vi = vf Use the constant velocity equation:

For an object at rest: vi = 0 m/s. For an object that stops: vf = 0 m/s. Examine the known variables before deciding which equation to use to solve the problem. Don’t be too surprised if you have to use one equation to find a variable and then use a second equation to get the desired answer!