Question: need answer not need to much explanation 3. Using definite and indefinite integration, solve the problems in sub-tasks (a), (b) and (c). (a) The velocities
need answer not need to much explanation

3. Using definite and indefinite integration, solve the problems in sub-tasks (a), (b) and (c). (a) The velocities (v) of two vehicles with the same starting position $ att = 0, travelling in the same direction, are given by the equations below: V1 = 3t + 2 m/s V2 = 2t2 - 4t m/s (i) Derive an expression for the distance travelled by each vehicle, s, and s, in terms of t and S. (ii) Initially one of the vehicles will move ahead but the other will catch up and overtake. When does this happen? (b) At time t = 0 seconds, an 80 V d.c. supply (V) is connected across a coil of inductance 4 H (L) and resistance 10 Q (R). Growth of current (?) in the inductance is given by the formula: i= 1- 0 amps A current of 1 amp of represents a flow of 1 coulomb of charge per second. Using definite integration, find the total charge (Q) passing through the circuit in the period t = 0.3 to t = 1 seconds. (c) The velocity in metres per second v of a car at time t seconds after the brakes are applied is given by: v = 15e- m/s Predict the distance the vehicle will travel in the first two seconds of braking
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