Avehicle of ‘dry’ mass m0, with no propulsion, is moving without friction on hor- izontal ground. rain is falling vertically. while the rain is falling, for each time interval ∆t, an amount of rain ∆mr = b∆t hits the vehicle, sticks to it, and then moves along with zero relative velocity with respect to the vehicle. the vehicle is observed to be slowing down. in a reference system fixed to the ground, at time t = 0, the cart is initially moving with speed v0. (a) at time t, the vehicle is traveling with speed v(t). for the time interval [t, t+∆t], while the rain is falling, determine a differential relation for the change in speed of the vehicle ∆v. write your answer using some or all of the following: t, ∆t, m0 and b. (b) integrate your result from part (a) to find the speed v(t) of the cart at time t. write your answer using some or all of the following: v0, b, m0 and t.