# Motion along a line (Rectilinear Motion) Help

• Loppyfoot
In summary, the conversation was about a student's difficulty understanding velocity, acceleration, and speed. They attached pictures from their textbook to help explain the problem and requested assistance with parts a, b, c, and d. They also asked for someone to help them sketch a graph of the velocity and provided instructions on how to do so. It was mentioned that the acceleration is the derivative of the velocity and can be estimated by graphing the slope of the tangent line at different points.
Loppyfoot
Alright, so I attached pictures of the problem from my textbook. I thought it would make it easier for you to help me.

I am having trouble picturing the velocity, acceleration and speed. If someone could help me through a, b, c, and d, I would love the help.

Thanks

#### Attachments

• scan0001.jpg
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• scan0002.jpg
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Anyone available to help?

a. The particle is moving right if the position (x value) is increasing, and moving to the left if the position is decreasing.

When the tangent to the graph of x(t) is horizontal, the particle is stopped. Can you sketch a rough graph of the velocity v(t) of the particle? You can do this by estimating the slope of the tangent line at a few points and plotting those values.

The acceleration a(t) is the derivative of the velocity. If you have a graph of the velocity, you can estimate the slope of the tangent line at a few points, and graphing them.

## 1. What is rectilinear motion?

Rectilinear motion refers to the motion of an object along a straight line. This means that the object is moving in one direction and does not deviate from that path.

## 2. What is the difference between rectilinear motion and curvilinear motion?

Rectilinear motion occurs when an object moves along a straight line, while curvilinear motion occurs when an object moves along a curved path. Rectilinear motion is simpler to analyze and calculate, while curvilinear motion involves more complex calculations.

## 3. What are the key variables in rectilinear motion?

The key variables in rectilinear motion are displacement, velocity, and acceleration. Displacement is the change in position of the object, velocity is the rate of change of displacement, and acceleration is the rate of change of velocity.

## 4. How is rectilinear motion represented mathematically?

Rectilinear motion can be represented using equations such as s = ut + 1/2at^2 for displacement, v = u + at for velocity, and a = (v-u)/t for acceleration. Here, s represents displacement, u represents initial velocity, v represents final velocity, a represents acceleration, and t represents time.

## 5. What are some real-life examples of rectilinear motion?

Some examples of rectilinear motion in everyday life include a car moving along a straight road, a person walking in a straight line, and a ball falling vertically to the ground. These all involve motion along a straight line with constant or changing velocity and acceleration.

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