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Chapter 3: Problem 9

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

Short Answer

Expert verified
Yes, it is possible for an object to be moving in one direction but accelerating in another. The direction of the acceleration is determined by the direction of the change in velocity of an object, not by the direction of the motion itself. Therefore, the object's acceleration can be in a completely different direction from its movement. A prime example of this is a falling object: although it moves downwards, it accelerates upwards due to gravity.

Step by step solution

01

Understand velocity and acceleration

The first step is to understand what is meant by velocity and acceleration. Velocity is a vector quantity, which means it has both direction and magnitude. It describes the speed of the object and the direction of its movement. Acceleration, on the other hand, is the rate of change of velocity in respect to time. Therefore, it is possible for an object to be moving in one direction but accelerating in another.
02

About the falling object

Now consider an object falling under the influence of gravity. Perhaps the most common example of this phenomenon would be an object being dropped from a certain height. Although the object is moving downwards, it is accelerating in the upwards direction.
03

Why is the falling object accelerating upwards?

This is because the force of gravity that is pulling it downwards is also causing it to speed up, or accelerate. Although the object is indeed moving downwards (in the direction of the ground), it is accelerating upwards (away from the ground). This is because gravity is constantly pulling the object down, increasing its velocity as it descends, hence causing an acceleration in the opposite direction.

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Most popular questions from this chapter

A projectile has horizontal range \(R\) on level ground and reaches maximum height \(h .\) Find an expression for its initial speed.

A basketball player is 15 ft horizontally from the center of the basket, which is \(10 \mathrm{ft}\) off the ground. At what angle should the player aim the ball from a height of \(8.2 \mathrm{ft}\) with a speed of \(26 \mathrm{ft} / \mathrm{s} ?\).

The New York Wheel is the world's largest Ferris wheel. It's 183 meters in diameter and rotates once every 37.3 min. Find the magnitudes of (a) the average velocity and (b) the average acceleration at the wheel's rim, over a 5.00 -min interval. (c) Compare your answer to (b) with the wheel's instantaneous accelerations.

A migrating whale follows the west coast of Mexico and North America toward its summer home in Alaska. It first travels 360 km northwest to just off the coast of northern California, and then turns due north and travels \(400 \mathrm{km}\) toward its destination. Determine graphically the magnitude and direction of its displacement.

You're designing a "cloverleaf" highway interchange. Vehicles will exit the highway and slow to a constant \(70 \mathrm{km} / \mathrm{h}\) before negotiating a circular turn. If a vehicle's acceleration is not to exceed \(0.40 g\) (i.e., \(40 \%\) of Earth's gravitational acceleration), then what's the minimum radius for the turn? Assume the road is flat, not banked (more on this in Chapter 5 ).
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