Questions: A car travels along a straight path for 16 minutes. How far is the car from the start when it is done? Distance from start = ? km

Transcript text: A car travels along a straight path for 16 minutes. How far is the car from the start when it is done? Distance from start = $\square$ ? ] km

Solution

Solution Steps

Step 1: Calculate the displacement during the first 2 minutes.

The velocity is changing from 0 to 2 km/min, so the displacement is (1/2) * (0+2) * 2 = 2 km.

Step 2: Calculate the displacement from 2 minutes to 3 minutes.

The velocity changes from 2 to 0 km/min, covering a displacement of (1/2) * (2+0) * 1 = 1 km.

Step 3: Calculate the displacement from 3 minutes to 4 minutes.

The velocity changes from 0 to 3 km/min giving a displacement of (1/2) * (0+3) * 1 = 1.5 km.

Step 4: Calculate the displacement from 4 minutes to 7 minutes.

The velocity remains constant at 3 km/min for 3 minutes giving a displacement of 3*3 = 9 km.

Step 5: Calculate the displacement from 7 minutes to 10 minutes.

The velocity is changing from 3 to 0 km/min, giving a displacement of (1/2) * (3+0) * 3 = 4.5 km.

Step 6: Calculate the displacement from 10 minutes to 12 minutes.

The velocity changes from 0 to -2 km/min giving a displacement of (1/2) * (0 + (-2)) * 2 = -2 km.

Step 7: Calculate the displacement from 12 minutes to 16 minutes.

The velocity is constant at -2 km/min for 4 minutes, giving a displacement of -2 * 4 = -8 km.

Step 8: Calculate the total displacement.

The total displacement is 2 + 1 + 1.5 + 9 + 4.5 - 2 - 8 = 7 km.

Final Answer

7 km

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