CALC? At time t = 0 a 2150-kg rocket in outer space fires an engine that exerts an increasing force on it in the +x-direction. This force obeys the equation Fx = At2, where t is time, and has a magnitude of 781.25 N when t = 1.25 s. (a) Find the SI value of the constant A , including its units. (b) What impulse does the engine exert on the rocket during the 1.50-s interval starting 2.00 s after the engine is fired? (c) By how much does the rocket’s velocity change during this interval? Assume constant mass.
Solution 11E Step 1: Data given Mass m = 2150 kg t1= 0 s Force exerted F = 781.25 N t2= 1.25 s Condition given Fx = At 2 We need to find the SI unit for A Consider Fx = At 2 Substituting values we get 781.25 N x = A × (1.25 s) 2 Hence we 2 A = (781.25 N )/(1.25 s) 2 A = 500 N/s Step 2 : We need to find the impulse exerted by the engine We know impulse as I = F × t 2 But we have F =xAt Thus we have 2 I = At × t 2 2 I = 500 × (2.0 + 1.25 )N × (2.0)s 2 2 I = 500 × (2.0 + 1.25 )N × (2.0)s I = 2781.25N × 2.0s I = 5810 Ns Hence we get the impulse as 5810 Ns