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  • A particle starts with a velocity of 2 m/s and moves in a straight line with retardation of 0.1 m/s2. The time (in seconds) at which the particle is 15 m from the starting point is<d

A particle starts with a velocity of 2 m/s and moves in a straight line with retardation of 0.1 m/s2. The time (in seconds) at which the particle is 15 m from the starting point is

Option: 1

10


Option: 2

25


Option: 3

20


Option: 4

40


Answers (1)

best_answer

\\ \text{Given :}\\ \text{Displacement},S =15 m\\ \text{Initial velocity},u=2 \ m/s^{2} \\ \text{Retardation},a= -0.1 \ m/s^{2}=\frac{1}{10} \ m/s^{2} \\ \text{From equation of motion}, \\ S=ut+\frac{1}{2}at^{2} \\ \\15=2t-\frac{1}{2}\left ( \frac{1}{10} \right )t^{2} \\ \\15=2t-\frac{t^{2}}{20} \\\\ 15=\frac{40t-t^{2}}{20}\\\\300=40t-t^{2} \\\\\Rightarrow t^{2}-40t+300=0

\\ \Rightarrow t^{2}-30t-10t+300=0 \\ \Rightarrow \left ( t-30 \right )\left ( t-10 \right ) \\ \\ \Rightarrow t=10s , 30s

\\ \text{Here we got two value of time i.e. 10s and 30s} \\ \text{Now we calculate at what time velocity of particle become zero(due to retardation) } \\ v=u+at\\0=2-0.1t\\t=20 s \ \ \ \ \ \left [ \text{At t=20s velocity become zero and it moves in the backward direction} \right ] \\ \\ \text{ Thus, in the next 30s , the particle will again have a displacement of 15 m .} \\ \\\text{Thus, In 10 s e c the particle will have a displacement of 15m firstly.} \\ \text{Hence, 10 sec is the correct answer.}

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