# Question-68609

Question Number 68609 by TawaTawa last updated on 14/Sep/19
Commented by TawaTawa last updated on 14/Sep/19
$$\mathrm{I}\:\mathrm{got}\:\mathrm{4m}/\mathrm{s}^{\mathrm{2}} \:\:\:\mathrm{in}\:\mathrm{number}\:\mathrm{14},\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{check} \\$$
Answered by mr W last updated on 14/Sep/19
$$\left(\mathrm{13}\right) \\$$$${s}={t}^{\mathrm{3}} −{t}^{\mathrm{2}} −{t}−\mathrm{2} \\$$$${v}=\frac{{ds}}{{dt}}=\mathrm{3}{t}^{\mathrm{2}} −\mathrm{2}{t}−\mathrm{1} \\$$$${a}=\frac{{dv}}{{dt}}=\mathrm{6}{t}−\mathrm{2} \\$$$${a}_{{ave}} =\frac{\int_{\mathrm{2}} ^{\mathrm{4}} {a}\left({t}\right){dt}}{\mathrm{4}−\mathrm{2}}=\frac{\left[\mathrm{3}{t}^{\mathrm{2}} −\mathrm{2}{t}\right]_{\mathrm{2}} ^{\mathrm{4}} }{\mathrm{2}}=\frac{\mathrm{32}}{\mathrm{2}}=\mathrm{16}\:{m}/{s}^{\mathrm{2}} \\$$$${or} \\$$$${a}\left(\mathrm{4}\right)=\mathrm{6}×\mathrm{4}−\mathrm{2}=\mathrm{22} \\$$$${a}\left(\mathrm{2}\right)=\mathrm{6}×\mathrm{2}−\mathrm{2}=\mathrm{10} \\$$$${a}_{{ave}} =\frac{\mathrm{22}+\mathrm{10}}{\mathrm{2}}=\mathrm{16}\:{m}/{s}^{\mathrm{2}} \\$$$$\\$$$$\left(\mathrm{14}\right) \\$$$$\mathrm{3}{t}^{\mathrm{2}} −\mathrm{2}{t}−\mathrm{1}=\mathrm{0} \\$$$$\left(\mathrm{3}{t}+\mathrm{1}\right)\left({t}−\mathrm{1}\right)=\mathrm{0} \\$$$$\Rightarrow{t}=\mathrm{1}\: \\$$$${a}\left(\mathrm{1}\right)=\mathrm{6}×\mathrm{1}−\mathrm{2}=\mathrm{4}\:{m}/{s}^{\mathrm{2}} \\$$
Commented by TawaTawa last updated on 14/Sep/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\mathrm{i}\:\mathrm{appreciate} \\$$