The t- axis is represent is A. The total distance travelled by the car in the first ten seconds. Therefore, A. The total distance travelled by the car in the first ten seconds is correct .
The area under the curve y = f(t) and above the t-axis on the interval [0, 10] represents the total distance traveled by the car in the first ten seconds. This is because the speed of the car is represented by the function f(t), and the area under the curve represents the total distance traveled.
Another way to think about it is that the speed is the rate of change of the distance. So, if we integrate the speed function, we get the distance function. In this case, the distance function is the area under the curve y = f(t).
Here is a more detailed explanation:
Option B. The acceleration of the car is incorrect because the acceleration is the rate of change of the speed, not the total distance traveled.
Option C. The average velocity of the car in the first ten seconds is incorrect because the average velocity is calculated by dividing the total distance traveled by the time elapsed. In this case, we are only given the speed function, not the distance function.
Option D. The velocity of the car is incorrect because the velocity is the speed of the car at a specific point in time. In this case, we are asked to find the total distance traveled in the first ten seconds, which is represented by the area under the curve.