As a car passes the point A on a straight road, its speed is 10 m s. The car moves with constant acceleration am s2 along the road for T seconds until it reaches the point B, where its speed is V m s1. The car travels at this speed for a further 10 seconds, when it reaches the point C. From C it travels for a further T seconds with constant acceleration 3a ms2 until it reaches a speed of 20 m s1 at the point D. Sketch the (r,v) graph for the motion, and show that V = 12.5. Given that the distance between A and D is 675 m, find the values of a and T. (OCR)

Title: As a car passes the point A on a straight road, its speed is 10 m s.

Accelerated Journey: (r,v) Graph Analysis

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Scope: Unraveling Acceleration, Speed, and Distance Dynamics

1. Introduction: As a car passes the point A on a straight road, its speed is 10 m s…..

• The motion of a car unfolds along a straight road, characterized by varying speeds, constant accelerations, and distinct points denoted by A, B, C, and D. This exploration navigates the intricacies of the car’s journey, focusing on acceleration, speed, and the resulting (r,v) graph.

2. Scenario Description:

• The car’s journey is delineated into segments, with constant acceleration, varied speeds at specific points, and intervals marked by T seconds. The objective is to sketch the (r,v) graph, demonstrate the derivation of V (speed at point B), and calculate the values of acceleration ‘a’ and time ‘T’ based on the given distance between points A and D.

3. Objectives:

• The primary objectives include sketching the (r,v) graph, showcasing the derivation of V (speed at point B), and calculating the values of acceleration ‘a’ and time ‘T’ based on the overall distance covered.

4. Significance:

• The significance lies in deciphering the interplay between constant acceleration, varied speeds, and distance, offering insights into the nuanced dynamics of the car’s journey along the straight road.

5. Exploration Focus:

• The exploration centers on understanding the relationships between acceleration, speed, and distance, visualizing these dynamics through the (r,v) graph, and employing mathematical calculations to determine key parameters.

6. Dynamics of Motion:

• Core dynamics involve analyzing the car’s motion in distinct segments, identifying the effects of constant acceleration, varied speeds, and the resulting characteristics reflected in the (r,v) graph.

7. Sketching the (r,v) Graph:

• Analysis includes the visual representation of the car’s journey through the (r,v) graph, capturing the changing dynamics at each point (A, B, C, D) and illustrating the transitions in speed and position.

8. Derivation of V:

• The exploration showcases the derivation of V, the speed at point B, demonstrating how the car’s characteristics influence its velocity at specific instances during the journey.

Douglas Quadling Mechanics1 Miscellaneous Exercise1 Q4

As a car passes the point A on a straight road, its speed is 10 m s……..

Calculating a and T:

• Mathematical calculations form an integral part of the exploration, leading to the determination of acceleration ‘a’ and time ‘T’ based on the provided distance between points A and D.

Conclusion:

As a car passes the point A on a straight road, its speed is 10 m s……….

• The exploration promises to unveil the intricacies of the car’s journey through the (r,v) graph, deriving key parameters and shedding light on the calculated dynamics of acceleration, speed, and distance in this accelerated motion scenario.

The Next Question: https://alevelmechanics1.com/600/the-figure-shows-the-rv-graph-for-the-motion-of-a-cyclist/