Question

a self propelled vehicle of mass M and whose engine delivers constant power P has an acceleration a =P/Mv.to increase the velocity of vehicle from v1 to v2 the distance travelled by it is​

Answer 1

Answer:

The answer will be M/3P (v2^3 - v1^3)

Explanation:

According to the problem the mass of the vehicle is given as M and the power of the engine of the vehicle is given as P

The acceleration of the vehicle ,a is also given

let us consider the vehicle is in origin at initial state, and at this state the velocity is v1 m/s

It will covered a distance of x after that its velocity will be v2m/s

Now we know that acceleration , a = v dv/dx

                                                  => P/Mv =  v dv/dx

                                                   => P/M dx = v^2 dv

now integrating both side

∫P/M dx [0 to x] = ∫ v^2 dv [ v1 to v2]

=> P/M x = v2^3 - v1^3/3

=> x = M/3P (v2^3 - v1^3)