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A particle moves along a straight line with constant acceleration, changing speed from $10\text{ m/s}$ to $20\text{ m/s}$ while covering $135\text{ m}$. The time taken is:
Using $v^2 - u^2 = 2as$: $(20)^2 - (10)^2 = 2a(135) \Rightarrow 300 = 270a \Rightarrow a = \dfrac{10}{9}\text{ m/s}^2$
Using $v = u + at$: $20 = 10 + \dfrac{10}{9}t \Rightarrow t = \mathbf{9\text{ s}}$
Density $\rho = 4\ \text{g/cm}^3$. We need to convert this to the new unit system.
New unit of mass: $100\ \text{g}$, New unit of length: $10\ \text{cm}$
New unit of density $= \dfrac{100\ \text{g}}{(10\ \text{cm})^3} = \dfrac{100\ \text{g}}{1000\ \text{cm}^3} = 0.1\ \text{g/cm}^3$
Numerical value in new system $= \dfrac{4\ \text{g/cm}^3}{0.1\ \text{g/cm}^3} = 40$
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