Question

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

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

Step-by-step solution

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.

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 \(-1.1\,\mathrm{m/s} \times 3.5\,\mathrm{s} = -3.85\,\mathrm{m}\).

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: \(7.3\,\mathrm{m} - 3.85\,\mathrm{m} = 3.45\,\mathrm{m}\).

Key concepts

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.