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| PAGE: 376 | SET: Exercises | PROBLEM: 16 |
Velocity graph of an accelerating car is shown.
(a)
Determine the average velocityof the car using the mid point rule during the first 
seconds.
Average value of the function 
on 
is defined as 
.
Average velocity of the car is 
.
Consider the number of subintevals 
.
Width of the interval 
.
Mid points are 
and 
.
.
Substitute 
and corresponding velocity values from the graph.
Substitute above result in 
.
Average velocity of the car is 
Km/h.
(b)
Find at what time instantaneous velocity is equal to the average velocity.
The condition nedd to check is 
.
We have, 
.
Observe the graph to determine at which interval of time corresponding velocity is 
Km/h.
From the graph, it is clear that at 
sec, instantaneous velocity is equal to the average velocity.
(a) Average velocity of the car is Km/h.
(b)
At 
sec, instantaneous velocity is equal to the average velocity.
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