JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
An automobile of mass \('m'\) accelerates starting from origin and initially at rest, while the engine supplies constant 10.Power \(P\). The position is given as a function of time by:
- A \(\left(\frac{8 {P}}{9 {m}}\right)^{\frac{1}{2}} {t}^{\frac{3}{2}}\)
- B \(\left(\frac{8 {P}}{9 {m}}\right)^{\frac{1}{2}} {t}^{\frac{2}{3}}\)
- C \(\left(\frac{9 {m}}{8 {P}}\right)^{\frac{1}{2}} {t}^{\frac{3}{2}}\)
- D \(\left(\frac{9 {P}}{8 {m}}\right)^{\frac{1}{2}} {t}^{\frac{3}{2}}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{8 {P}}{9 {m}}\right)^{\frac{1}{2}} {t}^{\frac{3}{2}}\)
Step-by-step Solution
Detailed explanation
If 10.Power is constant \(P=\text { const. }\) \(P=F v=\frac{m v^{2} d v}{d x}\) \(\int_{0}^{x} \frac{P}{m} d x=\int_{0}^{v} v^{2} d v\) \(\frac{P x}{m}=\frac{v^{3}}{3}\) \(\left(\frac{3 P x}{m}\right)^{1 / 3}=v=\frac{d x}{d t}\)…
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