A body initially at rest is acted upon by a constant force (F) for time (t). The kinetic energy at time…

A body initially at rest is acted upon by a constant force (F) for time (t). The kinetic energy at time $\mathrm{t}$ is
  1. $\frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}}$
  2. $\left(\frac{\mathrm{Ft}}{\mathrm{m}}\right)^{2}$
  3. $\frac{\mathrm{Ft}}{2 \mathrm{~m}}$
  4. $\frac{\mathrm{F}^{2} \mathrm{t}^{2}}{2 \mathrm{~m}}$

Solution

acceleration $\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}$ At time t, velocity $\mathrm{v}=\mathrm{at}=\frac{\mathrm{Ft}}{\mathrm{m}}$ Kinetic energy $=\frac{1}{2} \mathrm{mv}^{2}$ $=\frac{1}{2} \mathrm{~m} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}^{2}}=\frac{1}{2} \frac{\mathrm{F}^{2} \mathrm{t}^{2}}{\mathrm{~m}}$ ^

Asked in: MHT CET 2020 (14 Oct Shift 1)

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