A car goes 4 m/s for 10 seconds then speeds up to 12 m/s in two seconds. The car continues at this speed for a minute. The car then accelerates at -3 m/s" for 10 seconds How far did the car go in each time interval?

 To find out how far the car went in each time interval, we need to calculate the distance for each phase of its journey using the appropriate formula for each type. The formula for distance when speed is constant is \( \text{distance} = \text{speed} \times \text{time} \), and for acceleration, the distance is calculated using the formula \( \text{distance} = \text{initial speed} \times \text{time} + \frac{1}{2} \times \text{acceleration} \times \text{time}^2 \).

Phase 1 - Constant Speed of 4 m/s for 10 seconds: Distance = Speed × Time Distance = 4 m/s × 10 s = 40 m

Phase 2 - Acceleration from 4 m/s to 12 m/s in 2 seconds: We can calculate the acceleration first, using \( \text{acceleration} = \frac{ \text{change in speed} }{ \text{time} } \) Acceleration = (12 m/s - 4 m/s) / 2 s = 8 m/s² / 2 s = 4 m/s²

Then we can calculate the distance covered during this acceleration phase, Distance = Initial Speed × Time + (1/2) × Acceleration × Time² Distance = 4 m/s × 2 s + (1/2) × 4 m/s² × (2 s)² Distance = 8 m + (1/2) × 4 m/s² × 4 s² Distance = 8 m + 2 m/s² × 4 s² Distance = 8 m + 2 m/s² × 16 s² Distance = 8 m + 32 m Distance = 40 m

Phase 3 - Constant Speed of 12 m/s for 60 seconds (1 minute): Distance = Speed × Time Distance = 12 m/s × 60 s = 720 m

Phase 4 - Deceleration at -3 m/s² for 10 seconds: Deceleration means the car is slowing down, so the acceleration is negative (-3 m/s²).

Distance = Initial Speed × Time + (1/2) × Acceleration × Time² Distance = 12 m/s × 10 s + (1/2) × (-3 m/s²) × (10 s)² Distance = 120 m + (1/2) × (-3 m/s²) × 100 s² Distance = 120 m - 1.5 m/s² × 100 s² Distance = 120 m - 150 m Distance = -30 m (Negative because it's slowing down, however, the distance traveled can't actually be negative, so we take the absolute value) Distance = 30 m

Adding up the distances for all phases gives us the total distance the car has traveled:

Total Distance = Distance Phase 1 + Distance Phase 2 + Distance Phase 3 + Distance Phase 4 Total Distance = 40 m + 40 m + 720 m + 30 m Total Distance = 830 m

So, the car went 40 m in Phase 1, 40 m in Phase 2, 720 m in Phase 3, and 30 m in Phase 4.