A car is moving in the positive direction along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, when does the position where the average speed equals the instantaneous speed occur during the time interval from A to B? Assume the time interval is T.Select one:a.after T/2 from the start of the intervalb.T/2 from the start of the intervalc.It depends on the speed at the start of the time interval.d.before T/2 from the start of the interval
Question
A car is moving in the positive direction along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, when does the position where the average speed equals the instantaneous speed occur during the time interval from A to B? Assume the time interval is T.Select one:a.after T/2 from the start of the intervalb.T/2 from the start of the intervalc.It depends on the speed at the start of the time interval.d.before T/2 from the start of the interval
Solution
The correct answer is a. after T/2 from the start of the interval.
Here's why:
The average speed of an object is defined as the total distance traveled divided by the total time elapsed. The instantaneous speed is the speed of an object at a particular moment in time.
In a scenario where a car is accelerating at a constant rate, the instantaneous speed is continuously increasing. This means that for the majority of the time interval, the instantaneous speed will be less than the average speed.
However, as the car continues to accelerate, there will come a point where the instantaneous speed equals the average speed. This point will occur after the halfway point (T/2) of the time interval. This is because the average speed, which takes into account the slower speeds at the beginning of the interval, will be lower than the instantaneous speed, which is continuously increasing.
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