The velocity-time graph of a body of mass 4 kg moving along a straight line is shown in figure. Work done by all the forces acting on the body from \( t=0 \) to \( t=5s \) is
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A decreasing velocity trend automatically indicates that the net work done on the system must be negative, as the body is losing kinetic energy due to dissipative braking forces.
Step 1: Choose the right tool. The question asks for the work done by all forces together. The work energy theorem says this net work equals the change in kinetic energy of the body. So we only need the starting and ending speeds. Step 2: Write the theorem. \[ W_{net} = \frac{1}{2}mv_f^{2} - \frac{1}{2}mv_i^{2} \] Step 3: Read the data from the graph. The mass is $m = 4$ kg. At $t = 0$ the speed is $v_i = 20\ ms^{-1}$. At $t = 5$ s the speed has dropped to $v_f = 10\ ms^{-1}$. Step 4: Put the numbers in. \[ W = \frac{1}{2}(4)\left[(10)^{2} - (20)^{2}\right] \] Step 5: Work out the brackets. \[ W = 2\left[100 - 400\right] = 2(-300) \] Step 6: Get the final value. The speed went down, so kinetic energy fell and the net work is negative: \[ \boxed{W = -600\ \text{J}} \]
