Question 110: Work, Energy and Power & Circular Motion

Question

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

Accepted Answer

P = const.
$$P = Fv = {{m{v^2}dv} \over {dx}}$$
$$\int\limits_0^x {{P \over m}dx}  = \int\limits_0^v {{v^2}dv} $$
$${{Px} \over m} = {{{v^3}} \over 3}$$
$${\left( {{{3Px} \over m}} \right)^{1/3}} = v = {{dx} \over {dt}}$$
$${\left( {{{3P} \over m}} \right)^{1/3}}\int\limits_0^t {dt}  = \int\limits_0^x {{x^{ - 1/3}}} dx$$
$$ \Rightarrow x = {\left( {{{8P} \over {9m}}} \right)^{1/2}}{t^{3/2}}$$

Answer

$${\left( {{{9P} \over {8m}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}$$

Answer

$${\left( {{{8P} \over {9m}}} \right)^{{1 \over 2}}}{t^{{2 \over 3}}}$$

Answer

$${\left( {{{9m} \over {8P}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}$$

Answer

$${\left( {{{8P} \over {9m}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}$$

Work, Energy and Power & Circular Motion

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

Choose the correct answer: