Final answer:
A moving cart at a constant speed in a circle experiences centripetal acceleration directed towards the circle's center with zero tangential acceleration.
Step-by-step explanation:
A cart that is moving at a constant speed in a circle has centripetal acceleration towards the center of the circle, and because it is moving at constant speed, the tangential acceleration along the path is zero. The centripetal acceleration is always directed towards the center of the circle and is necessary for the cart to remain in circular motion, as it causes the continuous change in direction of the velocity vector. Without this acceleration, the cart would continue in a straight line due to inertia, as per Newton's first law of motion.
The term 'centripetal' comes from the Latin words 'centrum' (meaning "center") and 'petere' (meaning "to seek"), signifying that this acceleration is "center seeking." Even though the speed of the cart is constant, which implies no change in magnitude of velocity, the perpetual change in velocity's direction necessitates acceleration, which is entirely centripetal in the case of uniform circular motion.