To find the law connecting ( R ) and ( V ), we can set up a relationship between them based on the given information.Let's denote the constant resistance as ( R_0 ) and the resistance that varies with the square of the speed as ( R_v ). So, the total resistance ( R ) can be expressed as:[ R = R_0 + R_v ]Given that ( R_0 ) is constant and ( R_v ) varies with the square of the speed ( V ), we can express ( R_v ) as ( kV^2 ), where ( k ) is a constant.So, the law connecting ( R ) and ( V ) is:[ R = R_0 + kV^2 ]Now, we can use the given data to find the values of ( R_0 ) and ( k ).When the car is moving at 20 km/h, ( R = 720 ) ohms:[ 720 = R_0 + k(20)^2 ]And when the car is moving at 60 km/h, ( R = 2320 ) ohms:[ 2320 = R_0 + k(60)^2 ]Now, we have a system of two equations that we can solve to find ( R_0 ) and ( k ).Solving these equations will give us:[ R_0 = 200 , \text{ohms} ] [ k = 0.1 , \text{ohms/km}^2 ]Now, we can use this information to find the resistance at 40 km/h.[ R = R_0 + k(40)^2 ] [ R = 200 + 0.1 \times (40)^2 ] [ R = 200 + 0.1 \times 1600 ] [ R = 200 + 160 ] [ R = 360 , \text{ohms} ]So, the resistance at 40 km/h is 360 ohms.
