TS EAMCET · Physics · Motion In One Dimension
A particle moving along \(X\)-axis has acceleration \(f\) at time \(t\) given by \(f=f_0\left(1-\frac{t}{T}\right)\), where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0\), the particle's velocity is
- A \(\frac{1}{2} f_0 T^2\)
- B \(f_0 T^2\)
- C \(\frac{1}{2} f_0 T\)
- D \(f_0 T\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2} f_0 T\)
Step-by-step Solution
Detailed explanation
Acceleration of the particle is given as \(f=f_0\left(1-\frac{t}{T}\right)\) \(\ldots(\mathrm{i})\) \(\therefore\) Velocity of particle is given as, \(v=\int f d t=\int f_0\left(1-\frac{t}{T}\right) d t=f_0\left(t-\frac{t^2}{2 T}\right)+c\) \(\ldots(\mathrm{ii})\) Given that, at…
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