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Q.

A car begins to move at time t = 0 and then accelerates along a straight track with a speed given by $v (t) = 2 t^{2} {ms}^{- 1} for 0 \leq t \leq 2$
After the end of acceleration, the car continues to move at a constant speed. A small block initially at rest on the floor of the car begins to slip at t =1s and stops slipping at t = 3s . Find the coefficient of kinetic friction between the block and the floor.

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answer is 0.3.

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$\begin{array}{ll} \Rightarrow m \frac{dv}{dt} = m (4 t) - μ_{k} mg \\ \Rightarrow \int_{0}^{0} dv = \int_{1}^{2} 4 tdt - \int_{1}^{3} μ_{k} gdt \end{array}$
$\begin{array}{ll} \Rightarrow [V]_{0}^{0} = 4 {[\frac{t^{2}}{2}]}_{1}^{2} - μ_{k} g [t]_{1}^{3} \\ \Rightarrow 0 - 0 = 4 (\frac{3}{2}) - μ_{k} (10) (2) \\ \Rightarrow μ_{k} = 0 .3 \end{array}$

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A car begins to move at time t = 0 and then accelerates along a straight track with a speed given by v(t)=2t2ms−1 for 0≤t≤2 After the end of acceleration, the car continues to move at a constant speed. A small block initially at rest on the floor of the car begins to slip at t =1s and stops slipping at t = 3s . Find the coefficient of kinetic friction between the block and the floor.