QuestionProblem 12.46 The acceleration of a sled can be prescribed to have one of the following forms: $a=\beta_{1} \sqrt{t}, a=\beta_{2} t$, and $a=\beta_{3} t^{2}$, where $t$ is time expressed in seconds, $\beta_{1}=1 \mathrm{~m} / \mathrm{s}^{5 / 2}, \beta_{2}=1 \mathrm{~m} / \mathrm{s}^{3}$, and $\beta_{3}=1 \mathrm{~m} / \mathrm{s}^{4}$. The sled starts from rest at $t=0$. Determine which of the three cases allows the sled to cover the largest distance in 1 s . In addition, determine the distance covered for the case in question.
Figure P12.45 and P12.46 Answm