Kinematics

JEE Main level, single correct, medium

70 of 308

Question 70 of 308

A particle has an initial velocity 3i^+4j^3 \hat{i}+4 \hat{j} and an acceleration of 0.4i^+0.3j^0.4 \hat{i}+0.3 \hat{j}. Its speed after 10 s is

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Answer: (B) 727 \sqrt{2} units

u→=3i^+4j^;a→=0.4i^+0.3j^u→=u→+a→t=3i^+4j^+(0.4i^+0.3j^)10=3i^+j^+4i^+3j^=7i^+7j^\begin{aligned} \overrightarrow{\mathrm{u}} & =3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} ; \overrightarrow{\mathrm{a}}=0.4 \hat{\mathrm{i}}+0.3 \hat{\mathrm{j}} \\ \overrightarrow{\mathrm{u}} & =\overrightarrow{\mathrm{u}}+\overrightarrow{\mathrm{a}} \mathrm{t} \\ & =3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+(0.4 \hat{\mathrm{i}}+0.3 \hat{\mathrm{j}}) 10=3 \hat{i}+\hat{\mathrm{j}}+4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}=7 \hat{\mathrm{i}}+7 \hat{\mathrm{j}} \end{aligned}
Speed is 72+72=72\sqrt{7^2+7^2}=7 \sqrt{2} units

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