MHT CET · Physics · Laws of Motion
A body initially at rest is acted upon by a constant force (F) for time (t). The kinetic energy at time \(\mathrm{t}\) is
- A \(\frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}}\)
- B \(\left(\frac{\mathrm{Ft}}{\mathrm{m}}\right)^{2}\)
- C \(\frac{\mathrm{Ft}}{2 \mathrm{~m}}\)
- D \(\frac{\mathrm{F}^{2} \mathrm{t}^{2}}{2 \mathrm{~m}}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{F}^{2} \mathrm{t}^{2}}{2 \mathrm{~m}}\)
Step-by-step Solution
Detailed explanation
acceleration \(\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}\)
At time t, velocity \(\mathrm{v}=\mathrm{at}=\frac{\mathrm{Ft}}{\mathrm{m}}\)
Kinetic energy \(=\frac{1}{2} \mathrm{mv}^{2}\)
\(=\frac{1}{2} \mathrm{~m} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}^{2}}=\frac{1}{2} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}}\)
At time t, velocity \(\mathrm{v}=\mathrm{at}=\frac{\mathrm{Ft}}{\mathrm{m}}\)
Kinetic energy \(=\frac{1}{2} \mathrm{mv}^{2}\)
\(=\frac{1}{2} \mathrm{~m} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}^{2}}=\frac{1}{2} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}}\)
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