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Chapter 2: Problem 16

Can an object's acceleration be in the opposite direction to its motion? Explain.

Short Answer

Expert verified
Answer: Yes, an object's acceleration can be in the opposite direction of its motion. This occurs when the object is experiencing a deceleration or negative acceleration, causing it to slow down and potentially change direction. Examples include a car braking and an object being thrown upwards and eventually falling back down due to gravity.

Step by step solution

01

Understanding motion, velocity, and acceleration

Motion is an object's change in position over time. Velocity is the rate of change of an object's position with respect to time (i.e., how fast it is moving). It has both magnitude (speed) and direction. Acceleration is the rate of change of velocity with respect to time, which means it can indicate a change in an object's speed or direction of motion or both.
02

Investigate the relationship between velocity and acceleration

When an object's velocity and acceleration are in the same direction, the object's speed increases, and it continues to move in the same direction. When an object's velocity and acceleration are in opposite directions, this means the object is slowing down in its present direction and may come to a stop or even reverse direction if the acceleration continues to act in the opposite direction for a sufficient amount of time.
03

Can the acceleration be in the opposite direction of motion?

Yes, an object's acceleration can be in the opposite direction of its motion. This occurs when the object is experiencing a deceleration or negative acceleration. This causes the object to slow down in the direction it is moving, and if the deceleration continues over time, the object may eventually come to a stop or reverse direction.
04

Examples

A common example of acceleration in the opposite direction of motion is when a car is braking. The velocity of the car is initially in the forward direction, and when the brakes are applied, the acceleration (i.e., the force acting on it) is in the opposite direction to decrease its speed. Similarly, when an object is thrown upwards, gravity acts as an acceleration in the opposite direction, causing the object to slow down, stop, and eventually reverse direction and fall back down to the ground. In conclusion, an object's acceleration can indeed be in the opposite direction of its motion, which leads to the object decelerating and potentially changing direction.

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Most popular questions from this chapter

An airplane starts from rest and accelerates at \(12.1 \mathrm{~m} / \mathrm{s}^{2}\). What is its speed at the end of a \(500 .-\mathrm{m}\) runway?

An electron moves in the positive \(x\) -direction a distance of \(2.42 \mathrm{~m}\) in \(2.91 \cdot 10^{-8} \mathrm{~s}\), bounces off a moving proton, and then moves in the opposite direction a distance of \(1.69 \mathrm{~m}\) in \(3.43 \cdot 10^{-8} \mathrm{~s}\). a) What is the average velocity of the electron over the entire time interval? b) What is the average speed of the electron over the entire time interval?

A particle starts from rest at \(x=0\) and moves for \(20 \mathrm{~s}\) with an acceleration of \(+2.0 \mathrm{~cm} / \mathrm{s}^{2}\). For the next \(40 \mathrm{~s}\), the acceleration of the particle is \(-4.0 \mathrm{~cm} / \mathrm{s}^{2} .\) What is the position of the particle at the end of this motion?

Starting from rest, a boat increases its speed to \(5.00 \mathrm{~m} / \mathrm{s}\) with constant acceleration. a) What is the boat's average speed? b) If it takes the boat 4.00 s to reach this speed, how far has it traveled?

The vertical position of a ball suspended by a rubber band is given by the equation $$ y(t)=(3.8 \mathrm{~m}) \sin (0.46 t / \mathrm{s}-0.31)-(0.2 \mathrm{~m} / \mathrm{s}) t+5.0 \mathrm{~m} $$ a) What are the equations for velocity and acceleration for this ball? b) For what times between 0 and \(30 \mathrm{~s}\) is the acceleration zero?
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