Acceleration

Definition of Acceleration An acceleration is the change in velocity per unit of time. (A vector quantity.) A change in velocity requires the application of a push or pull (force). A formal treatment of force and acceleration will be given later. For now, you should know that: The direction of accel- eration is same as direction of force. The acceleration is proportional to the magnitude of the force.

Acceleration and Force Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force.

Acceleration (+) vs. Deceleration (-) +x F + a+ v+ Car is accelerating Car is decelerating F - a- v+

Example of Acceleration + vf = +8 m/s vi = +2 m/s t = 3 s Force The wind changes the speed of a boat from 2 m/s to 8 m/s in 3 s. Each second the speed changes by 2 m/s. Wind force is constant, thus acceleration is constant.

The Signs of Acceleration Acceleration is positive (+) or negative (-) based on the direction of force. Choose + direction first. Then acceleration a will have the same sign as that of the force F —regardless of the direction of velocity. + F a (-) F a(+)

+ Force t = 4 s vi = +8 m/s vf = +20 m/s Example 1 (No change in direction): A constant force changes the speed of a car from 8 m/s to 20 m/s in 4 s. What is the acceleration of the car? + Force t = 4 s vi = +8 m/s vf = +20 m/s Step 1. Draw a rough sketch. Step 2. Choose a positive direction (right). Step 3. Label given info with + and - signs. Step 4. Indicate direction of force F.

Example 1 (cont.): What is the car’s acceleration? + vi = +8 m/s t = 4 s vf = +20 m/s Force Step 5. Recall definition of the acceleration. a = + 3m/s2 to the right