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In summary, the individual needs help with solving problems and verifying their answers. They specifically request assistance with drawing a velocity versus time graph and mention that the average gradient represents constant acceleration. They also mention the equation for distance traveled as velocity multiplied by time, and note that the area bounded by the duration on the graph is relevant. The individual is advised to show their attempt at solving the problems in order to receive targeted help and to develop the ability to verify their own answers.

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The average gradient is the constant acceleration.

Distance travalled is velocity χ time. From the graph is the area bounded by the duration.

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You will get the best results from here by showing us your attempt - this allows us to target our help to where you actually need it so avoiding wasting time for both of us.

Your main problem is the need to have someone else verify your answers. This is a problem because you are supposed to be training to handle problems where nobody knows the answers - who will verify your answers then? You need a way to verify the answers for yourself - unless we know where you get stuck we cannot help you with that.

Motion in one dimension refers to the movement of an object along a single straight line. This means that the object's position can only be described by one coordinate, typically denoted as x. In contrast, motion in multiple dimensions involves movement in two or three dimensions, meaning the object's position can be described by two or three coordinates, such as x and y or x, y, and z.

The main types of motion in one dimension are constant velocity motion, where the object moves at a constant speed in a straight line, and accelerated motion, where the object's speed or direction changes over time. Accelerated motion can be further divided into two types: uniform acceleration, where the object's speed changes by the same amount in each time interval, and non-uniform acceleration, where the object's speed changes by varying amounts in each time interval.

Displacement refers to the change in an object's position from its initial position to its final position. It is a vector quantity and is typically denoted as Δx. Distance, on the other hand, refers to the total length travelled by an object during its motion. It is a scalar quantity and is typically denoted as d. While displacement takes into account the direction of motion, distance does not.

Speed refers to the rate at which an object covers a certain distance, while velocity refers to the rate at which an object changes its position. Speed is a scalar quantity and is typically denoted as v, while velocity is a vector quantity and is typically denoted as v with an arrow on top. This means that velocity takes into account both the speed and direction of an object's motion.

To graph motion in one dimension, we plot the position of the object on the y-axis and time on the x-axis. The resulting graph is called a position-time graph or a displacement-time graph. The slope of this graph represents the object's velocity at any given point, as velocity is equal to the change in position over the change in time. The area under the graph represents the object's displacement during the given time interval. A horizontal line on the graph represents constant velocity motion, while a curved line represents accelerated motion.

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