Acceleration, Speed, and Velocity - MCAT

SPEED vs VELOCITY

As far as speed is concerned, remember that speed is a scalar (just a number) and velocity is a vector (a number and a direction). You could come up with a situation where there is no change in speed but a change in velocity. That situation would be a particle moving in a circle without speeding up or slowing down (i.e., uniform circular motion). The velocity will be changing because the particle is not moving in a straight line. Even though the numerical value of the velocity isn’t changing, the direction part is changing, and therefore the velocity is also changing.

ACCELERATION, VELOCITY, AND SPEED

Acceleration is defined as a change in velocity over some time.

So if the net force is not zero, then every single time without fail no matter what, the acceleration is not zero and the velocity is changing.

If the net force is constant, the acceleartion is constant and the velocity is changing at a constant rate.

Say you have a constant acceleration of 10 m/s^2 down.

Every second, you add 10 m/s down to your previous velocity vector. If you start out going 5 m/s down, in 1 second you’ll be going 15 m/s down, in two you’ll be going 25 m/s down, etc….

If you have non-zero acceleration, but it is NOT constant, your velocity vector will change, but it will change different amounts every second. Eg, start out at 5 m/s down, next second your at 40 m/s down, the next second you’re at 2 m/s to the left.

Again, if the acceleration is constant, and it is not zero, there IS a change in velocity. Always, every single time, no matter what. It could be a change in the direction, the speed, or both. On the MCAT, acceleration problems will generally be constant non-zero acceleration. All of those problems will involve a change in velocity. Everyone, everytime, every year, every MCAT administration. Now repeat after me:

"Acceleration IS a change in velocity. If there is acceleration, the velocity is changing."

HINT:

Try to stop thinking about speed. Speed doesn’t really make sense. If you’re going 50 mph, do you care what direction you are going? Yes, of course you do. Doing your thing around town do you ever care about speed without direction? No.

Speed is an abstract silly thing that is used when bragging about the Porsche they give you if you get a 45 on the MCAT. In physics and real life, you always deal with direction at the same time, so you want to think about velocity.