Question

A brake mechanism used to reduce recoil in certain types of heavy duty shocks consists essentially of a piston that is attached to the shock body and may move in a fixed cylinder filled with oil. As the shock body recoils with an initial velocity v0, the piston moves, and oil is forced through orifices in the piston, causing the piston and the shock body to decelerate at a rate  proportional to their velocity ( a=f(v) = -kv.)

Initial conditions:

x0=0 m

v0= 10 m/s at t=0 s

v= 1 m/s at t=1 s.

Determine:

1. x in terms of v using integration
2. t in terms of v
3. k
4. x in terms of t
5. a in terms of t
6. x,v, and a for t=0.5 s

Use Appropriate Units

Answer 1