Can someone please solve this problem step by step? A race car with mass of 300K

Question

Can someone please solve this problem step by step? A race car with mass of 300Kg is driven by a force withmagnitude F(t)=270t^2 and moves along a straight line. a) What is the impulse after t=3 seconds? b) If the car starts from rest what is the cars speed (inMiles/hour) at t=3s? c) What will the cars speed be after 6 seconds? Can someone please solve this problem step by step? A race car with mass of 300Kg is driven by a force withmagnitude F(t)=270t^2 and moves along a straight line. a) What is the impulse after t=3 seconds? b) If the car starts from rest what is the cars speed (inMiles/hour) at t=3s? c) What will the cars speed be after 6 seconds?

Explanation / Answer

Impulse J = integral F ( t ) dt                = 270 * t ^ 3 / 3                = 90 t ^ 3 (a). impulse after 3 seconds J = 90 ( 3 ^ 3 )                                              = 2430 kg m / s (b). initial speed u = 0 m / s we know J = m( v - u )                J = m v from this speed at time t = 3 s is v = J / m                                                      = 2430 / 300                                                     = 8.1 m / s (c). impulse after 6 s is J ' = 90 ( 6 ^ 3 )                                         = 19440 kg m / s So, speed at time t = 6 s is v ' = J ' / m                                                = 64.8 m / s

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