$\"\"$

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Velocity graph of an accelerating car is shown.

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(a)

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Determine the average velocityof the car using the mid point rule during the first $\"\"$ seconds.

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Average value of the function $\"\"$ on $\"\"$ is defined as $\"\"$ .

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Average velocity of the car is $\"\"$ .

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Consider the number of subintevals $\"\"$ .

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Width of the interval $\"\"$ .

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Mid points are $\"\"$ and $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and corresponding velocity values from the graph.

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$\"\"$

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$\"\"$

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Substitute above result in $\"\"$ .

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$\"\"$

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Average velocity of the car is $\"\"$ Km/h.

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$\"\"$

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(b)

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Find at what time instantaneous velocity is equal to the average velocity.

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The condition nedd to check is $\"\"$ .

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We have, $\"\"$ .

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Observe the graph to determine at which interval of time corresponding velocity is $\"\"$ Km/h.

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From the graph, it is clear that at $\"\"$ sec, instantaneous velocity is equal to the average velocity.

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$\"\"$

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(a) Average velocity of the car is $\"\"$ Km/h.

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(b) At $\"\"$ sec, instantaneous velocity is equal to the average velocity.