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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
It is possible for an object to be moving in one direction but accelerating in another, particularly in the case of circular motion. In this instance, the object’s velocity is directed in the direction of motion (tangent to the circle), while its acceleration (the rate of change of direction of velocity) is directed towards the centre of the circle. This is due to the concept of centripetal acceleration.

Step by step solution

01

Understand Definitions

In physics, velocity is a vector quantity that describes the speed and direction of an object. On the other hand, acceleration is the rate of change of velocity per unit of time; it is also a vector quantity, having both magnitude and direction. So, an object can move in one direction (its velocity), while its acceleration (rate of change of velocity) can be in a different direction.
02

Picture an Example

One common example of this situation is an object moving in a circle, like a car traveling around a circular track. At any given point along the track, the car's velocity is tangent to the circle (along the direction of motion), but its acceleration (due to change in direction of velocity) is towards the centre of the circle. This happens because even though the speed of the car might be constant, the direction is constantly changing which results in a radial acceleration.
03

Understand the Concept

This can be explained by the concept of centripetal acceleration. In circular motion, the acceleration of an object is always directed towards the centre of the circle. This idea is the basis of the concept of centripetal acceleration. Although the object’s speed may be constant, its velocity is continually changing because its direction of motion is continually changing. Thus, an object moving in a circle is accelerating even if its speed is constant.

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Most popular questions from this chapter

An object is initially moving in the \(x\) -direction at \(4.5 \mathrm{m} / \mathrm{s}\), when it undergoes an acceleration in the \(y\) -direction for a period of \(18 \mathrm{s}\) If the object moves equal distances in the \(x\) - and \(y\) -directions during this time, what's the magnitude of its acceleration?

The singapore Flyer is the world's largest Ferris wheel. Its diameter is \(150 \mathrm{m}\) and it rotates once every 30 min. Find the magnitudes of (a) the average velocity and (b) the average acceleration at the wheel's rim, over a 5.0 -min interval.

A particle's position is \(\vec{r}=\left(c t^{2}-2 d t^{3}\right) \hat{\imath}+\left(2 c t^{2}-d t^{3}\right) \hat{\jmath}\) where \(c\) and \(d\) are positive constants. Find expressions for times \(t>0\) when the particle is moving in (a) the \(x\) -direction and (b) the \(y\) -direction.

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You throw a baseball at a \(45^{\circ}\) angle to the horizontal, aiming at a friend who's sitting in a tree a distance \(h\) above level ground. At the instant you throw your ball, your friend drops another ball. (a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value, (b) Find an expression for that minimum speed,
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