Separate variables. [ \fracdv2 - 0.1v = dt ]

That’s a classic variable acceleration problem. The solutions manual for Ch. 11 is correct, but let me clarify the logic.

Solve for ( v(t) ) using initial condition (usually ( v_0 ) at ( t=0 )). The manual then often uses ( v = dx/dt ) to find ( x(t) ) with a second integration.

Integrate both sides. The manual’s key move: substitute ( u = 2 - 0.1v ), so ( du = -0.1, dv ) → ( dv = -10, du ). [ \int \frac-10, duu = \int dt ] [ -10 \ln|u| = t + C ] [ -10 \ln|2 - 0.1v| = t + C ]

Set up the differential equation. [ \fracdvdt = 2 - 0.1v ]

The isn’t just an answer key—it’s a tutorial. Here’s what makes Chapter 11 unique and how to use the solutions effectively.

Chapter 11 of Beer & Johnston’s Vector Mechanics for Engineers: Dynamics (11th Ed.) introduces the fundamental concepts of kinematics —the geometry of motion without considering forces. This chapter is the bedrock for all future dynamics topics.

If you’re an engineering student staring down Chapter 11 of Beer & Johnston’s Dynamics , you already know: kinematics is the gatekeeper. Get through this, and the rest of dynamics (Newton’s laws, work-energy, impulse-momentum) becomes manageable. Fail here, and you’re lost.