Work out an estimate for the total distance covered by the ball.
How to approach this question
1. Understand that the distance covered is the area under the velocity-time graph.
2. Split the graph into simpler shapes. A good way is to split it at t=4 and t=10. This gives you a curved section, a rectangle, and a triangle.
3. Calculate the area of the rectangle and the triangle using standard formulas.
4. Estimate the area of the curved section. You can do this by approximating it as a trapezium or by counting squares.
5. Add the areas of the three sections together to get the total estimated distance.
Full Answer
The total distance covered by the ball is equal to the area under the velocity-time graph. We can split the graph into three sections from t=0 to t=16.
**Section 1: t = 0 to t = 4 (Curved section)**
This part is a curve. We can estimate its area by treating it as a trapezium. The "height" of the trapezium is the time interval (4 - 0 = 4). The parallel sides are the velocities at t=0 and t=4.
Velocity at t=0 is 0 m/s.
Velocity at t=4 is 8 m/s.
Area₁ ≈ ½ × (sum of parallel sides) × height
Area₁ ≈ ½ × (0 + 8) × 4 = 16 m.
**Section 2: t = 4 to t = 10 (Rectangle)**
This is a rectangle with width (10 - 4 = 6) and height 8.
Area₂ = width × height = 6 × 8 = 48 m.
**Section 3: t = 10 to t = 16 (Triangle)**
This is a triangle with base (16 - 10 = 6) and height 8.
Area₃ = ½ × base × height = ½ × 6 × 8 = 24 m.
**Total Distance:**
Total Distance = Area₁ + Area₂ + Area₃
Total Distance ≈ 16 + 48 + 24 = 88 m.
Common mistakes
✗ Forgetting to divide by 2 when calculating the area of the triangle.
✗ Incorrectly calculating the width of the rectangle or the base of the triangle.
✗ Using an incorrect method to estimate the area under the curve.
✗ Reading values incorrectly from the graph axes.
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