A particle at rest starts moving with acceleration \(a_1\). Until it reaches the speed \(v\), it immediately decelerates with \(a_2\) until it stops. The total time consumed is \(t\). Show that the displacement of the particle is \(\frac{1}{2}vt\).
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Comments
It can also be interpreted as :
Draw the velocity vs time graph of the particle. We need to find the area under the graph which is the area of the triangle which simply is 21× base × height =21⋅t⋅v. This is the required value.
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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
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to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
It can also be interpreted as :
Draw the velocity vs time graph of the particle. We need to find the area under the graph which is the area of the triangle which simply is 21× base × height =21⋅t⋅v. This is the required value.
Can be easily proved using v Vs t graph
The average velocity with first is (0+v)/2=v/2, in second case it is (v+0)/2=v/2 same as first.
So d = (average velocity)*Time.