# Acceleration

When an object's velocity vector is changing, the object is*accelerating*. Examples include a car speeding up ("accelerating" in common parlance), slowing down or braking ("decelerating", but physicists prefer to say "negatively accelerating"), and turning. In three dimensions, we define acceleration by

(3a)

(3b)

The units for acceleration are [(m/s)/s = m/s Â· 1/s = m/s^{2}].

Take north to be positive. A car is traveling south and speeding up. What is the sign of the acceleration?

Since the velocity vector points south and the car is speeding up, the acceleration vector must point south. With this sign convention, acceleration is negative.

Take north to be positive. A car traveling south speeds up from 10 m/s to 15 m/s in 10 s. What is its acceleration?

We write

This confirms our thinking in Example 1a.

Take north to be positive. A car is traveling north and slowing for a red light. What is the sign of the acceleration?

The velocity vector points north. Since this vector is shrinking, the acceleration vector must point south. Thus the acceleration is negative.

What is the acceleration for the car in Example 2a slowing from 10 m/s to 8 m/s in 1 s?

We write

An Oldsmobile takes a certain amount of time to accelerate from 0 to 60 mph. A Porsche takes less time by a factor of 3 to accelerate from 0 to 60 mph. How does the Porsche acceleration compare with that of the Oldsmobile?

We look at equation (4)

Since Î”*v* is constant, if Î”*t* is smaller by a factor of 3, then *a* is larger by a factor of 3.