Math  /  Calculus

Question17. The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.

Studdy Solution

STEP 1

1. The velocity-time graph is a continuous function.
2. The area under the velocity-time graph represents the distance traveled.
3. The graph is a downward-sloping curve, indicating deceleration.

STEP 2

1. Understand the relationship between velocity, time, and distance.
2. Estimate the area under the velocity-time graph.
3. Calculate the distance using the estimated area.

STEP 3

The velocity-time graph shows how the velocity of the car changes over time. The area under this graph represents the total distance traveled by the car while braking.

STEP 4

To estimate the area under the curve, we can use geometric shapes such as rectangles, trapezoids, or triangles to approximate the area.

STEP 5

Divide the time interval from 0 to 6 seconds into smaller sub-intervals. For simplicity, consider dividing it into 6 intervals of 1 second each.

STEP 6

For each 1-second interval, estimate the velocity at the beginning and end of the interval. Use these values to form trapezoids or rectangles to approximate the area under the curve.

STEP 7

Calculate the area of each trapezoid or rectangle. For a trapezoid, use the formula: Area=12×(Base1+Base2)×Height\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} where Base1\text{Base}_1 and Base2\text{Base}_2 are the velocities at the beginning and end of the interval, and Height\text{Height} is the time interval (1 second).

STEP 8

Sum the areas of all trapezoids or rectangles to get the total estimated area under the curve, which represents the total distance traveled.

STEP 9

The total estimated area under the velocity-time graph is the estimated distance traveled by the car while the brakes are applied.
The estimated distance traveled by the car while the brakes are applied is approximately the sum of the areas calculated in STEP_6. Since the exact graph is not provided, this is a conceptual approach to solving the problem.

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