Kinetic energy problem

on3winyoureyes

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I'm completely lost on this question:
[h=1]In physics, the kinetic energy of a moving object is given by the formula K=1/2mv^2 where m is the mass of the object and v is the object's velocity.Suppose a rocket is increasing in velocity at 10m/sec^2, and is decreasing in mass at 15kg/sec because it is using up fuel. How fast is it's total kinetic energy changing when the velocity is 30m/sec and the mass is 1000kg? Round to the nearest tenth.[/h]I know we have to find the derivative of the kinetic energy equation. and somehow plug dv/dt and dm/dt
 
I'm completely lost on this question:
In physics, the kinetic energy of a moving object is given by the formula K=1/2mv^2 where m is the mass of the object and v is the object's velocity.Suppose a rocket is increasing in velocity at 10m/sec^2, and is decreasing in mass at 15kg/sec because it is using up fuel. How fast is it's total kinetic energy changing when the velocity is 30m/sec and the mass is 1000kg? Round to the nearest tenth.

I know we have to find the derivative of the kinetic energy equation. and somehow plug dv/dt and dm/dt
Actually you haven't given enough information to solve the problem. The acceleration is a constant 10m/s2. Velocity is the integral of acceleration, i.e.
v = v0 + a (t-t0)
where v0 is the velocity at time t0. In the same way the rate of change of the mass is the derivative of the mass so that
v = m0 + b (t-t0)
where m0 is the mass at time t0. Using the product rule for the derivative of the kinetic energy K, you can see that v0, m0, and t0 appear in the solution. What are those values?
.
 
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