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A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in Fig. 7.37, a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block's speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?
Show Answer
(i) At 0 m: \(\tfrac{1}{2}mv^2 = 180 \Rightarrow v^2 = \dfrac{360}{10} = 36 \Rightarrow v = 6\ \text{m s}^{-1}\).
Work by the force = area under Fig. 7.37 \(= \tfrac{1}{2}(1)(50) + (2)(50) + \tfrac{1}{2}(1)(50) = 25 + 100 + 25 = 150\ \text{J}\).
(ii) KE at 4 m \(= 180 + 150 = 330\ \text{J} \Rightarrow v^2 = \dfrac{660}{10} = 66 \Rightarrow v = \sqrt{66} \approx 8.1\ \text{m s}^{-1}\).
The applied force stays in the direction of motion (always positive) throughout, so the block keeps speeding up — it has no negative acceleration in any portion.
