Explanation & Calculations
1). Velocity-time graph & consider the shown angle as "\\small \\theta"
Distance traveled is the area under the graph
"\\qquad \n\\begin{aligned}\n\\small \\text{Distance} &= \\small \\frac{1}{2}\\times 0.75s \\times15ms^{-1}\\\\\n\\small &= \\small \\bold{5.625m}\n\\end{aligned}"
2). Acceleration is the slope (gradient) of the graph = "\\small \\tan\\theta" & can be found using trigonometric relationships for the triangle under the curve.
"\\qquad \n\\begin{aligned}\n\\small \\text{Acceleration} &= \\small \\tan\\theta\\\\\n\\small \\text{but} \\tan(\\pi-\\theta) &= \\frac{15ms^{-1}}{0.75s}\\\\\n\\small -\\tan\\theta &= \\small 20ms^{-2}\\\\\n\\small \\tan\\theta &= \\small \\bold{-20ms^{-2}}\\\\\n\\small \\text{Deceleration} &= \\small \\bold{20ms^{-2}}\n\\end{aligned}"
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