A car starts from rest and moves along the path OAB as shown. It moves with a speed of 35 miles per hour along OA and 50 miles per hour along AB.
Which is true for the motion of the car during its journey along OAB?
somewhere between 35 and 50 mi/hr
No diagram, copy and paste will not work here.
Based on the information provided, the car starts from rest and moves along the path OAB. It moves with a speed of 35 miles per hour along OA and 50 miles per hour along AB.
The speed of the car along OA is 35 miles per hour, and the speed along AB is 50 miles per hour.
Since the car is starting from rest, it is accelerating along OA to reach a speed of 35 miles per hour. Once it reaches point A, the car is now moving at a constant speed of 35 miles per hour.
When the car reaches point B, it starts to accelerate again to reach a speed of 50 miles per hour.
So, during its journey along OAB, the car initially accelerates along OA, then maintains a constant speed along AB, and accelerates again along AB to reach a speed of 50 miles per hour.
To determine which statement is true for the motion of the car during its journey along OAB, we need to compare the car's acceleration along the two segments of the path.
Acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Since the car starts from rest, its initial velocity is 0.
Along OA, the car moves with a speed of 35 miles per hour. Let's denote the time taken to travel along OA as t1. Therefore, the final velocity V1 at the end of OA can be calculated as follows:
V1 = 35 miles per hour
acceleration along OA = (V1 - 0) / t1 = 35 miles per hour / t1
Similarly, along AB, the car moves with a speed of 50 miles per hour. Let's denote the time taken to travel along AB as t2. Therefore, the final velocity V2 at the end of AB can be calculated as follows:
V2 = 50 miles per hour
acceleration along AB = (V2 - V1) / t2 = (50 miles per hour - 35 miles per hour) / t2 = 15 miles per hour / t2
Now, we need to compare the accelerations along OA and AB to determine which statement is true:
1. The car accelerates along OA but decelerates along AB.
This statement is false because the car can only accelerate if the acceleration is positive. In this case, the acceleration along OA is positive (assuming time is positive), but the acceleration along AB is also positive because the velocity increases from V1 to V2.
2. The car accelerates along both OA and AB.
This statement is true because the car's velocity increases both along OA and AB, indicating positive accelerations along both segments.
3. The car decelerates along both OA and AB.
This statement is false because the car's velocity increases along both OA and AB, indicating positive accelerations along both segments.
Therefore, the correct answer is that the car accelerates along both OA and AB.