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What is the final position of an object that starts at \(7.3 \mathrm{~m}\) and moves with a velocity of \(-1.1 \mathrm{~m} / \mathrm{s}\) for \(3.5 \mathrm{~s}\) ?

Short Answer

Expert verified
The final position is \(3.45\,\mathrm{m}\).

Step by step solution

01

Identify Initial Position

The problem states that the object starts at an initial position of \(7.3\,\mathrm{m}\). This is the starting point for calculating the final position.
02

Determine Displacement

To find the displacement of the object, use the formula \( \text{displacement} = \text{velocity} \times \text{time} \). Here, the velocity is \(-1.1\,\mathrm{m/s}\) and the time is \(3.5\,\mathrm{s}\). Thus the displacement is \(-1.1\,\mathrm{m/s} \times 3.5\,\mathrm{s} = -3.85\,\mathrm{m}\).
03

Calculate Final Position

The final position is found by adding the displacement to the initial position. Since the displacement is negative, subtract the absolute value of the displacement from the initial position: \(7.3\,\mathrm{m} - 3.85\,\mathrm{m} = 3.45\,\mathrm{m}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Displacement
Displacement is a fundamental concept in kinematics. It refers to the change in position of an object from its initial point to its final point. It's important to understand that displacement is a vector quantity. This means it has both a magnitude and a direction.
In our problem, displacement can be calculated using the formula:
  • \( \text{displacement} = \text{velocity} \times \text{time} \)
A negative displacement, like in this exercise where we found \(-3.85 \, \mathrm{m}\), indicates that the movement is in the opposite direction to the reference direction. Always consider both direction and distance when evaluating displacement.
Velocity
Velocity plays a crucial role in motion analysis. It is not just about how fast something moves, but the direction of motion is equally important. This makes velocity a vector quantity.
In kinematics problems like ours, velocity helps us determine displacement over time:
  • Given velocity \(-1.1 \, \mathrm{m/s}\) tells us the object is moving in the negative or opposite reference direction.
  • When velocity is constant, computing displacement is straightforward with multiplication by time.
Understanding velocity in terms of both direction and speed is critical in solving motion-related problems accurately.
Initial Position
The initial position is the starting point from which any movement calculations begin. It's often denoted by a spatial coordinate and serves as a baseline for determining changes in position over time.
In our example, the initial position is given as \(7.3 \, \mathrm{m}\).
  • Knowing the initial position allows for calculating the final position effectively by taking into account any displacement.
  • If not directly stated, initial position can sometimes be inferred from context or other given information.
The way initial position and displacement interact is pivotal in determining where an object will be after certain conditions are met, such as time passing or velocities being applied.

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Most popular questions from this chapter

Triple Choice An object's position-time graph is a straight line with a positive slope. Is the velocity of this object positive, negative, or zero? Explain.

A bowling ball moves with constant velocity from an initial posi- tion of \(1.6 \mathrm{~m}\) to a final position of \(7.8 \mathrm{~m}\) in \(3.1 \mathrm{~s}\). (a) What is the position-time equation for the bowling ball? (b) At what time is the ball at the position \(8.6 \mathrm{~m}\) ?

Two football players move in a straight line directly toward one another. Their equations of motion are as follows: $$ \begin{aligned} &x_{1}=0.1 \mathrm{~m}+(-3.1 \mathrm{~m} / \mathrm{s}) t \\ &x_{2}=-6.3 \mathrm{~m}+(2.8 \mathrm{~m} / \mathrm{s}) t \end{aligned} $$ (a) Which player is moving faster? (b) At what time do the players collide?

Predict \& Explain You drive your car in a straight line at \(15 \mathrm{~m} / \mathrm{s}\) for \(10 \mathrm{~km}\), then at \(25 \mathrm{~m} / \mathrm{s}\) for another \(10 \mathrm{~km}\). (a) Is your average speed for the entire trip more than, less than, or equal to \(20 \mathrm{~m} / \mathrm{s}\) ? (b) Choose the best explanation from the following: A. More time is spent driving at \(15 \mathrm{~m} / \mathrm{s}\) than at \(25 \mathrm{~m} / \mathrm{s}\). B. The average of \(15 \mathrm{~m} / \mathrm{s}\) and \(25 \mathrm{~m} / \mathrm{s}\) is \(20 \mathrm{~m} / \mathrm{s}\). C. Less time is spent driving at \(15 \mathrm{~m} / \mathrm{s}\) than at \(25 \mathrm{~m} / \mathrm{s}\).

Calculate A golfer putts on the eighteenth green at a distance of \(5.0 \mathrm{~m}\) from the hole. The ball rolls straight, in the positive direction, but overshoots the hole by \(1.2 \mathrm{~m}\). The golfer then putts back to the hole and sinks the putt for par. (a) What is the distance traveled by the ball? (b) What is the displacement of the ball?

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