Thread: differential equations

1. A particle, of mass 0.4kg, is projected vertically upwards with an initial speed of 30 m/s. at time ts after projection, the speed of the particle is v m/s
and the magnitude of the air resistance acting on the particle is 0.2vN.

a) Show that, while the particle is ascending, v satisfies the differential equation



b) determine v in terms of t



Right so i'm a little new to differential equations so i'm unsure exactly what to do. I know that dv/dt is acceleration. I know that acceleration when the particle goes upwards verticle the force goes against gravity so thats where the -9.8 comes from. just not sure about the -0.5v


for part b i will take an educated guess that you have to integrate that equation, however its worth 6 marks so i think maybe theres more to it?

Originally Posted by djmccabie

1. A particle, of mass 0.4kg, is projected vertically upwards with an initial speed of 30 m/s. at time ts after projection, the speed of the particle is v m/s
and the magnitude of the air resistance acting on the particle is 0.2vN.

a) Show that, while the particle is ascending, v satisfies the differential equation



b) determine v in terms of t

(a) while traveling upward, net force on the particle ...



divide every term by ...



kg ... m/s^2




yes, integration is required for part (b) ...





separate variables ...



integrate both sides of the equation, use your initial condition to find the constant of integration, then finalize velocity as a function of time.