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Chapter 3: Problem 8

How is it possible for an object to be moving in one direction but accelerating in another?

Short Answer

Expert verified
Objects can move in one direction but accelerate in another when there are changes in speed or direction. For example, when a car moves forward but slows down, it is moving in one direction but accelerating in another (as deceleration). Additionally, objects moving in a circular path at a constant speed are always changing their direction, thereby, moving in one direction but accelerating towards the center of the circle.

Step by step solution

01

Understanding the Concepts of Velocity and Acceleration

Velocity is a vector quantity that indicates direction and speed of an object while acceleration refers to the rate of change of velocity. Acceleration can be a change in speed, a change in direction or both. Velocity and acceleration are independent, so they can occur in different directions.
02

Examples of Changes in Speed

Let's consider a car moving forward (specific direction) but slowing down. The car is in motion (velocity) forward but the speed (acceleration) is decreasing -- the latter is equivalent to acceleration in the opposite direction of motion. It's as if there's a force pulling it backwards, opposing its forward motion.
03

Examples of Changes in Direction

Now, let's consider a planet orbiting the sun in a circular path at a constant speed. Even though the speed is constant, the direction is always changing (velocity is changing) which implies the presence of an acceleration. The direction of the acceleration in this case is towards the center of the circle (the sun), hence the planet can be moving in one direction but accelerating in another.

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Most popular questions from this chapter

The New York Wheel is the world's largest Ferris wheel. It's 183 meters in diameter and rotates once every \(37.3 \mathrm{~min}\). Find the magnitudes of (a) the average velocity and (b) the average acceleration at the wheel's rim, over a \(5.00-\mathrm{min}\) interval. (c) Compare

An object's velocity is \(\vec{v}=c t^{3} \hat{\imath}+d \hat{\jmath}\), where \(t\) is time and \(c\) and \(d\) are positive constants with appropriate units. What's the direction of the object's acceleration?

Generalize Problem 90 to find an expression for the angle that will maximize the range of a projectile launched with speed \(v_{0}\) from height \(h\) above level ground.

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Find the magnitude of the vector \(31 \hat{\imath}+56 \hat{\jmath} \mathrm{m}\), and determine its angle to the \(x\)-axis.
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