14. A racing car accelerates uniformly through three gears, changes with the following average speed:

20 for 2.0 s
40 for 2.0 s
60 for 6.0 s

What is the overall average speed of the car?

12

your ans is 37m/s

To find the overall average speed of the car, we need to calculate the total distance covered by the car and the total time taken.

Let's start by calculating the distance covered in each gear:
In gear 1, the car travels at a speed of 20 m/s for 2.0 seconds. So the distance covered in gear 1 is:
Distance 1 = Speed 1 × Time 1 = 20 m/s × 2.0 s = 40 meters

In gear 2, the car travels at a speed of 40 m/s for 2.0 seconds. So the distance covered in gear 2 is:
Distance 2 = Speed 2 × Time 2 = 40 m/s × 2.0 s = 80 meters

In gear 3, the car travels at a speed of 60 m/s for 6.0 seconds. So the distance covered in gear 3 is:
Distance 3 = Speed 3 × Time 3 = 60 m/s × 6.0 s = 360 meters

Now, let's calculate the total distance covered by the car:
Total Distance = Distance 1 + Distance 2 + Distance 3 = 40 meters + 80 meters + 360 meters = 480 meters

Next, let's calculate the total time taken by the car:
Total Time = Time 1 + Time 2 + Time 3 = 2.0 s + 2.0 s + 6.0 s = 10.0 seconds

Finally, to find the overall average speed of the car, we divide the total distance by the total time:
Overall Average Speed = Total Distance / Total Time = 480 meters / 10.0 seconds ≈ 48 meters per second

So, the overall average speed of the car is approximately 48 meters per second.