AI Tutor
If you lock your car's cruise control at exactly 60 miles per hour and steer around a circular track, your speedometer never moves. Yet, in the language of physics, you are accelerating every single second.
How can an object accelerate without ever speeding up or slowing down?

Speed vs. Velocity in a Circle

A scalar is a quantity with only magnitude (size), like speed (vv), which tells you how fast an object travels. A vector is a quantity that has both magnitude and direction, like velocity (v⃗\vec{v}).
When an object travels along a circular path at a constant speed, this motion is called uniform circular motion.
At every point on the path, the velocity vector points tangent to the circle β€” directly in the instantaneous direction the object is traveling.
Because the path curves, the direction of that arrow changes continuously, meaning the velocity vector v⃗\vec{v} is never constant.
If velocity is constantly changing, what does the change in velocity vector actually look like?

The Vector Change: Why Acceleration Exists

Acceleration is the rate of change of velocity over time: aβƒ—=Ξ”vβƒ—Ξ”t\vec{a} = \frac{\Delta \vec{v}}{\Delta t}, where the change in velocity is Ξ”vβƒ—=vβƒ—2βˆ’vβƒ—1\Delta \vec{v} = \vec{v}_2 - \vec{v}_1.
To subtract two vectors geometrically, place their tails at the same point: the arrow pointing from the tip of v⃗1\vec{v}_1 to the tip of v⃗2\vec{v}_2 represents Δv⃗\Delta \vec{v}.