Finding distance through a velocity-time

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SUMMARY

The discussion focuses on calculating the distance traveled by a car using a velocity-time graph, specifically between the times of 0.60 seconds and 6.40 seconds. The car's velocity values are given as Vc = 4.00 m/s and Vd = 7.00 m/s. To find the distance, participants emphasize the importance of calculating the area under the graph, particularly addressing the trapezoidal area from 0.60 to 1 second and the area from 1 to 6.40 seconds. Techniques such as linear interpolation and the use of area formulas for trapezoids, rectangles, and triangles are recommended for accurate computation.

PREREQUISITES
  • Understanding of velocity-time graphs
  • Knowledge of area calculation for trapezoids and triangles
  • Familiarity with linear interpolation techniques
  • Basic concepts of kinematics and constant acceleration
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  • Study the formula for the area of a trapezoid
  • Learn about linear interpolation in physics
  • Explore kinematic equations for accelerated motion
  • Practice calculating areas under curves using various shapes
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Students in physics, educators teaching kinematics, and anyone interested in understanding motion analysis through velocity-time graphs.

Becca93
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Homework Statement



The graph attached shows the speed of a car traveling in a straight line as a function of time. The value of Vc is 4.00 m/s and the value of Vd is 7.00 m/s. Calculate the distance traveled by the car from a time of 0.60 to 6.40 seconds.


2&3. Relevant equations + Attempt at a solution
I know that the distance is the area under the graph. My and from t=1s to t=6.4s, I have the total. It's from t=0.6s to t=1s that I don't understand how to get.
 

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You have a straight line on the graph for the first second, so the acceleration is constant. You can find it (slope), then use an accelerated motion formula to find the velocity at time 0.6 s. Or use linear interpolation - 60% of the t=1 speed at t =0.6.

That leaves you with finding the area under the trapezoid from 0.6 to 1 s. Look up the formula in wikipedia if you don't know it. Or split it into a rectangle plus a triangle and use area formulas you do know.
 

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