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Standard XII

Physics

Speed Time Graph

Position-time...

Question

Position-time graph is shown, which is a semicircle from $t = 2$ to $t = 8$ sec. Find time $t$ at which the instantaneous velocity, is equal to average velocity over first $t$ seconds

4.8 sec

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3.2 sec

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2.4 sec

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5 sec

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Solution

The correct option is C 3.2 sec
Instantaneous velocity would be equal to the mean velocity when slope of the line joining final and initial point will be same as the slope of point on the curve.
Thus we get
$c o s θ = \frac{4}{5} = \frac{A O}{4}$
Thus we get $A O = 3.2 s e c$

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Position-time graph is shown, which is a semicircle from t=2 to t=8 sec. Find time t at which the instantaneous velocity, is equal to average velocity over first t seconds

The correct option is C 3.2 secInstantaneous velocity would be equal to the mean velocity when slope of the line joining final and initial point will be same as the slope of point on the curve.Thus we getcosθ=45=AO4Thus we get AO=3.2sec

Position-time graph is shown, which is a semicircle from $t = 2$ to $t = 8$ sec. Find time $t$ at which the instantaneous velocity, is equal to average velocity over first $t$ seconds

The correct option is C 3.2 sec
Instantaneous velocity would be equal to the mean velocity when slope of the line joining final and initial point will be same as the slope of point on the curve.
Thus we get
$c o s θ = \frac{4}{5} = \frac{A O}{4}$
Thus we get $A O = 3.2 s e c$