From Fig. 7.37, initial speed is 6 m s-1. The trapezoid area gives work done as 150 J, raising kinetic energy to 330 J and final speed to 8.12 m s-1. Acceleration is never negative since force stays positive.
A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in the 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?
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From Fig. 7.37, initial kinetic energy of 180 J yields an initial speed of 6 m s-1. The work done equals the area under the force-displacement graph, calculated as half times the sum of parallel sides 2 m and 4 m multiplied by height 50 N, giving 150 J. Final kinetic energy becomes 330 J, giving a speed of 8.12 m s-1 at 4 m. Acceleration remains non-negative throughout.
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