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Calculus Formula 1 cars produce enormous levels of downforce, which enables them to corner at very high speeds. However, there is a tradeoff to be made when designing such a car, which is that on the straight, high speed parts of the track the same components that produce downforce also produce drag, which slows the car down and reduces its top speed. The effect is more pronounced at high speed since drag squares with speed as per the following formula: 1 F CpA. In the formula above, F is the drag force (in Newtons); p is the density of the air (in kg/m³); v is the speed of the car (relative to the air, in m/s); A is the cross-sectional area (in m²); and Cp is the drag coefficient, a dimensionless constant that depends on various factors, including the Reynold's number and the shape of the car. For a typical Formula 1 car, the drag coefficient is around 1 (depending on the exact setup of the car)'. We can assume that the density of air is approximately 1 kg/m³ and the cross-sectional area of a Formula 1 car is about 2 m². In last weekend's Saudi Arabian Grand Prix Qualifying, Sergio Perez's Red Bull was fastest of all through the speed trap at 335 km/h (93 m/s). Assume that at the instant that he was travelling at 300 km/h (83 m/s) he was accelerating at 10Okm/h/s (3m/s²). At what rate (in N/s) was the drag force increasing at this instant?

Calculus Formula 1 cars produce enormous levels of downforce, which enables them to corner at very high speeds. However, there is a tradeoff to be made when designing such a car, which is that on the straight, high speed parts of the track the same components that produce downforce also produce drag, which slows the car down and reduces its top speed. The effect is more pronounced at high speed since drag squares with speed as per the following formula: 1 F CpA. In the formula above, F is the drag force (in Newtons); p is the density of the air (in kg/m³); v is the speed of the car (relative to the air, in m/s); A is the cross-sectional area (in m²); and Cp is the drag coefficient, a dimensionless constant that depends on various factors, including the Reynold's number and the shape of the car. For a typical Formula 1 car, the drag coefficient is around 1 (depending on the exact setup of the car)'. We can assume that the density of air is approximately 1 kg/m³ and the cross-sectional area of a Formula 1 car is about 2 m². In last weekend's Saudi Arabian Grand Prix Qualifying, Sergio Perez's Red Bull was fastest of all through the speed trap at 335 km/h (93 m/s). Assume that at the instant that he was travelling at 300 km/h (83 m/s) he was accelerating at 10Okm/h/s (3m/s²). At what rate (in N/s) was the drag force increasing at this instant?

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Calculus Formula 1 cars produce enormous levels of downforce, which enables them to corner at very high speeds. However, there is a tradeoff to be made when designing such a car, which is that on the straight, high speed parts of the track the same components that produce downforce also produce drag, which slows the car down and reduces its top speed. The effect is more pronounced at high speed since drag squares with speed as per the following formula: 1 F In the formula above, F is the drag force (in Newtons); p is the density of the air (in kg/m³); v is the speed of the car (relative to the air, in m/s); A is the cross-sectional area (in m?); and Cp is the drag coefficient, a dimensionless constant that depends on various factors, including the Reynold's number and the shape of the car. For a typical Formula 1 car, the drag coefficient is around 1 (depending on the exact setup of the car)'. We can assume that the density of air is approximately 1 kg/m³ and the cross-sectional area of a Formula 1 car is about 2 m². In last weekend's Saudi Arabian Grand Prix Qualifying, Sergio Perez's Red Bull was fastest of all through the speed trap at 335 km/h (93 m/s). Assume that at the instant that he was travelling at 300 km/h (83 m/s) he was accelerating at 10km/h/s (3m/s?). At what rate (in N/s) was the drag force increasing at this instant?
Transcribed Image Text:Calculus Formula 1 cars produce enormous levels of downforce, which enables them to corner at very high speeds. However, there is a tradeoff to be made when designing such a car, which is that on the straight, high speed parts of the track the same components that produce downforce also produce drag, which slows the car down and reduces its top speed. The effect is more pronounced at high speed since drag squares with speed as per the following formula: 1 F In the formula above, F is the drag force (in Newtons); p is the density of the air (in kg/m³); v is the speed of the car (relative to the air, in m/s); A is the cross-sectional area (in m?); and Cp is the drag coefficient, a dimensionless constant that depends on various factors, including the Reynold's number and the shape of the car. For a typical Formula 1 car, the drag coefficient is around 1 (depending on the exact setup of the car)'. We can assume that the density of air is approximately 1 kg/m³ and the cross-sectional area of a Formula 1 car is about 2 m². In last weekend's Saudi Arabian Grand Prix Qualifying, Sergio Perez's Red Bull was fastest of all through the speed trap at 335 km/h (93 m/s). Assume that at the instant that he was travelling at 300 km/h (83 m/s) he was accelerating at 10km/h/s (3m/s?). At what rate (in N/s) was the drag force increasing at this instant?
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