Acceleration straight line graph

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Homework Help Overview

The problem involves a particle that starts from rest and accelerates according to a provided graph. Participants are tasked with determining the particle's speed at specific times and the distance traveled over a given interval, while grappling with the implications of changing velocity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using the area under the acceleration graph to find speed and distance, while questioning the validity of their calculations. There is a mention of constant-acceleration equations and the desire for a reliable method, such as integration or graphical analysis.

Discussion Status

Some participants have provided guidance on using graphical methods to interpret the acceleration and velocity curves. Multiple interpretations of the problem are being explored, particularly regarding the effects of positive, negative, and zero acceleration on velocity.

Contextual Notes

There is an indication of confusion regarding the calculation of distance due to the changing velocity, and a reference to a textbook answer that differs from participants' calculations. The original poster expresses uncertainty about their approach and seeks clarification.

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Homework Statement


A particle starts from rest and accelerates as shown in the attached figure. Determine (a) the article's speed at t=10s and t=20s. (b) The distance traveled in the first 20s.


Homework Equations



a=dv/dt

The Attempt at a Solution


(a) t=10s, speed = 20m/s
t=20s, speed = 5m/s
Those were obtained by taking the area under the acceleration.

(b) book gives the answer 262m. NO idea how this came about. I thought about 225m being the answer since 20m/s * 10s + 5m/s * 5s, but this wouldn't be correct because the velocity is changing, not constant. Any help would be appreciated.
 

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You can use the constant-acceleration equations to work this out.
 
k is there a way by the graph or integration? I want to use something that's always going to work, if that's possible.
 
Graphically, the change in velocity from t1 to t2 represents the area under the acceleration curve.

After constructing a velocity curve, the change in displacement is the area under the velocity curve.

If the acceleration curve is positive, how does that affect velocity?
If the acceleration curve is negative, how does that affect velocity?
If the acceleration curve is zero, how does that affect velocity?
 

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