Acceleration straight line graph

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SUMMARY

The discussion focuses on calculating the speed and distance traveled by a particle under varying acceleration. At t=10s, the particle's speed is 20 m/s, while at t=20s, it is 5 m/s, determined by analyzing the area under the acceleration curve. The distance traveled in the first 20 seconds is stated to be 262 m, which contrasts with the incorrect estimate of 225 m based on constant velocity assumptions. The correct approach involves using the area under the velocity curve derived from the acceleration graph.

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  • Understanding of kinematics, specifically acceleration and velocity relationships
  • Familiarity with calculus concepts, particularly integration
  • Ability to interpret graphical data, especially acceleration and velocity curves
  • Knowledge of constant-acceleration equations
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  • Study the principles of integration in physics for calculating areas under curves
  • Learn about constructing velocity curves from acceleration data
  • Explore the implications of positive, negative, and zero acceleration on velocity
  • Review constant-acceleration equations and their applications in motion analysis
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Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators seeking to clarify concepts related to acceleration and velocity calculations.

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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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