From the Coroneos textbook.
18. i) A particle is moving along the x-axis. At time t, it is distant x from 0 and moving with velocity v = dx/dt.
Show that the acceleration dv/dt = v. dv/dx.
ii) The acceleration of a body moving in a straight line is proportional to the velocity, i.e. dv/dt = kv, where k is constant. When x = 0, v = 7 and when x = 3, v = 13. Find the value of v when x = 2.
{Hint, use the result in (i)}
If someone could solve this in a manner that I can comprehend, it would be much appreciated.
18. i) A particle is moving along the x-axis. At time t, it is distant x from 0 and moving with velocity v = dx/dt.
Show that the acceleration dv/dt = v. dv/dx.
ii) The acceleration of a body moving in a straight line is proportional to the velocity, i.e. dv/dt = kv, where k is constant. When x = 0, v = 7 and when x = 3, v = 13. Find the value of v when x = 2.
{Hint, use the result in (i)}
If someone could solve this in a manner that I can comprehend, it would be much appreciated.
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