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Chapter 1: Problem 22

As a car goes around a curve, the driver increases its speed. This means the car has two accelerations. What are the directions of these two accelerations?

Short Answer

Expert verified
Answer: The car experiences centripetal acceleration, directed towards the center of the curve, and tangential acceleration, directed forward along the curve in the direction of its instantaneous velocity.

Step by step solution

01

Determine the direction of centripetal acceleration

The centripetal acceleration is always directed towards the center of the curve the car is moving along. It's responsible for keeping the car in a curved path. As the car goes around the curve, the direction of centripetal acceleration continuously changes so that it always points towards the center of the curve.
02

Determine the direction of tangential acceleration

The tangential acceleration is directed along the car's instantaneous path (tangent to the curve) and is a result of the driver increasing the car's speed. In this case, the tangential acceleration is pointing in the same direction as the car's instantaneous velocity, meaning it's directed forward along the curve. So, in conclusion, there are two accelerations acting on the car as it goes around the curve and increases its speed: 1. Centripetal acceleration, directed towards the center of the curve. 2. Tangential acceleration, directed forward along the curve (in the direction of the car's instantaneous velocity).

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