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# Rocket driven car - Expression for acceleration

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A rocket-driven car of total mass M loses mass at a constant rate lembda per unit of time at a constant ejection speed V relative to the car. If the total resistance to motion is kv with the speed is v, show that the acceleration of the car along a straight horizontal road is (lembda V-kv) /(M- lambda t) at time t from the start. Hence show that the speed from rest is (lambda V/k)[1-(1- lambda t/M)^(k/lembda)].

https://brainmass.com/physics/acceleration/rocket-driven-car-expression-acceleration-159679

#### Solution Preview

Q4. A rocket-driven car of total mass M loses mass at a constant rate per unit of time at a constant ejection speed V relative to the car. If the total resistance to motion is kv with the speed is v, show that the acceleration of the car along a straight horizontal road is ( V-kv) /(M- t) at time t from the start. Hence show that the speed from rest is ( V/k)[1-(1- t/M)^(k/ )]

Solution : Total initial mass of the car = M
Rate of losing mass = Î»
Mass of the car at any time t = M - Î»t

As mass of the car reduces, its velocity ...

#### Solution Summary

The expression for acceleration for the rocket driven car is determined.

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