As an extension of Ex. 3.10, let the plate and cart be unrestrained, with frictionless wheels. Derive

Question:

As an extension of Ex. 3.10, let the plate and cart be unrestrained, with frictionless wheels. Derive (a) the equation of motion for cart velocity Vc (t); and (b) the time required for the cart to accelerate to 90% of jet velocity. (c) Compute numerical values for (b) using the data from Ex. 3.10 and a cart mass of 2 kg.