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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

A train traveling at \(40.0 \mathrm{~m} / \mathrm{s}\) is headed straight toward another train, which is at rest on the same track. The moving train decelerates at \(6.0 \mathrm{~m} / \mathrm{s}^{2},\) and the stationary train is \(100.0 \mathrm{~m}\) away. How far from the stationary train will the moving train be when it comes to a stop?

A ball is thrown straight upward in the air at a speed of \(15.0 \mathrm{~m} / \mathrm{s} .\) Ignore air resistance. a) What is the maximum height the ball will reach? b) What is the speed of the ball when it reaches \(5.00 \mathrm{~m} ?\) c) How long will it take to reach \(5.00 \mathrm{~m}\) above its initial position on the way up? d) How long will it take to reach \(5.00 \mathrm{~m}\) above its initial position on its way down?

The position versus time for an object is given as \(x=A t^{4}-B t^{3}+C\) a) What is the instantaneous velocity as a function of time? b) What is the instantaneous acceleration as a function of time?

An F-14 Tomcat fighter jet is taking off from the deck of the USS Nimitz aircraft carrier with the assistance of a steam-powered catapult. The jet's location along the flight deck is measured at intervals of \(0.20 \mathrm{~s} .\) These measurements are tabulated as follows: $$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline t(\mathrm{~s}) & 0.00 & 0.20 & 0.40 & 0.60 & 0.80 & 1.00 & 1.20 & 1.40 & 1.60 & 1.80 & 2.00 \\ \hline x(\mathrm{~m}) & 0.0 & 0.70 & 3.0 & 6.6 & 11.8 & 18.5 & 26.6 & 36.2 & 47.3 & 59.9 & 73.9 \\ \hline \end{array} $$ Use difference formulas to calculate the jet's average velocity and average acceleration for each time interval. After completing this analysis, can you say if the F- 14 Tomcat accelerated with approximately constant acceleration?

Consider three ice skaters: Anna moves in the positive \(x\) -direction without reversing. Bertha moves in the negative \(x\) -direction without reversing. Christine moves in the positive \(x\) -direction and then reverses the direction of her motion. For which of these skaters is the magnitude of the average velocity smaller than the average speed over some time interval?
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