{"id":642,"date":"2026-05-05T04:56:46","date_gmt":"2026-05-05T04:56:46","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/20-bai-toan-chuyen-dong-thuong-xuyen-xuat-hien-trong-de-thi\/"},"modified":"2026-05-05T07:31:19","modified_gmt":"2026-05-05T07:31:19","slug":"20-bai-toan-chuyen-dong-thuong-xuyen-xuat-hien-trong-de-thi","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/20-bai-toan-chuyen-dong-thuong-xuyen-xuat-hien-trong-de-thi\/","title":{"rendered":"20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi"},"content":{"rendered":"

T\u00e0i li\u1ec7u 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi<\/a> ch\u1ee9a 20 b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a v\u1eadt th\u1ec3 ho\u1eb7c xe c\u1ed9. M\u1ed7i b\u00e0i to\u00e1n \u0111\u1ec1u c\u00f3 c\u00e2u h\u1ecfi v\u00e0 \u0111\u00e1p \u00e1n k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft. C\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn v\u1eadn t\u1ed1c, gia t\u1ed1c, qu\u00e3ng \u0111\u01b0\u1eddng v\u00e0 th\u1eddi gian, s\u1eed d\u1ee5ng c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 t\u00edch ph\u00e2n \u0111\u1ec3 gi\u1ea3i quy\u1ebft. C\u00f9ng T\u00e0i Li\u1ec7u \u00d4n Thi<\/a> kh\u00e1m ph\u00e1 nh\u1eefng b\u00e0i to\u00e1n n\u00e0o c\u00f3 th\u1ec3 xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi n\u0103m nay nh\u00e9!<\/p>\n

N\u1ed9i dung 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi<\/h2>\n

D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 v\u1ec1 c\u00e1c d\u1ea1ng b\u00e0i to\u00e1n c\u00f3 trong t\u00e0i li\u1ec7u to\u00e1n 12<\/a> 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi:<\/p>\n

C\u00c2U 1<\/p>\n

M\u1ed9t ch\u1ea5t \u0111i\u1ec3m $A$ xu\u1ea5t ph\u00e1t t\u1eeb $O$, chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng v\u1edbi v\u1eadn t\u1ed1c bi\u1ebfn thi\u00ean theo th\u1eddi gian b\u1edfi quy lu\u1eadt $v(t) = \\frac{1}{100}t^2 + \\frac{13}{30}(m\/s)$, trong \u0111\u00f3 $t$ (gi\u00e2y) kho\u1ea3ng th\u1eddi gian t\u00ednh t\u1eeb l\u00fac $A$ b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng. T\u1eeb tr\u1ea1ng th\u00e1i ngh\u1ec9, m\u1ed9t ch\u1ea5t \u0111i\u1ec3m $B$ c\u0169ng xu\u1ea5t ph\u00e1t t\u1eeb $O$, chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng c\u00f9ng h\u01b0\u1edbng v\u1edbi $A$ nh\u01b0ng ch\u1eadm h\u01a1n 10 gi\u00e2y so v\u1edbi $A$ v\u00e0 c\u00f3 gia t\u1ed1c $a(m\/s^2)$ ($a$ l\u00e0 h\u1eb1ng s\u1ed1). Sau khi $B$ xu\u1ea5t ph\u00e1t \u0111\u01b0\u1ee3c 15 gi\u00e2y th\u00ec \u0111u\u1ed5i k\u1ecbp $A$.<\/p>\n

a) V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $B$ l\u00e0 $v_B(t) = at$ trong \u0111\u00f3 $t$ (gi\u00e2y) kho\u1ea3ng th\u1eddi gian t\u00ednh t\u1eeb l\u00fac $B$ b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng.
\nb) Qu\u00e3ng \u0111\u01b0\u1eddng ch\u1ea5t \u0111i\u1ec3m $A$ \u0111i \u0111\u01b0\u1ee3c trong 10 gi\u00e2y \u0111\u1ea7u l\u00e0 $25m$.
\nc) Qu\u00e3ng \u0111\u01b0\u1eddng ch\u1ea5t \u0111i\u1ec3m $B$ \u0111i \u0111\u01b0\u1ee3c trong 15 gi\u00e2y l\u00e0 $\\frac{225}{2}m$.
\nd) V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $B$ t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111u\u1ed5i k\u1ecbp $A$ l\u00e0 $25m\/s$.<\/p>\n

\u0110\u00e1p \u00e1n: \u0110\u00fang \u2013 \u0110\u00fang \u2013 Sai \u2013 \u0110\u00fang<\/p>\n

\n

L\u1eddi gi\u1ea3i<\/p>\n

a) $v_B(t) = \\int adt = at + C$<\/p>\n

$v_B(0) = 0 \\Leftrightarrow C = 0 \\Rightarrow v_B(t) = at (m\/s)$<\/p>\n

b) Qu\u00e3ng \u0111\u01b0\u1eddng A \u0111i \u0111\u01b0\u1ee3c trong 10s \u0111\u1ea7u l\u00e0:<\/p>\n

$S_1 = \\int_0^{10} v_A(t) dt = \\int_0^{10} \\left(\\frac{1}{100}t^2 + \\frac{13}{30}t\\right) dt = 25(m)$<\/p>\n

c) Qu\u00e3ng \u0111\u01b0\u1eddng B \u0111i trong 15s = Qu\u00e3ng \u0111\u01b0\u1eddng A \u0111i trong 25s.<\/p>\n

$\\Rightarrow S_2 = \\int_0^{25} v_A(t) dt = \\int_0^{25} \\left(\\frac{1}{100}t^2 + \\frac{13}{30}t\\right) dt = \\frac{375}{2}(m) (= AA\u2019)$<\/p>\n

d) $S_2 = \\int_0^{15} v_B(t) dt = \\int_0^{15} at dt = \\frac{at^2}{2}\\Big|_0^{15} = \\frac{a \\cdot 15^2}{2} (-BB\u2019)$<\/p>\n

M\u00e0 B \u0111u\u1ed5i k\u1ecbp A n\u00ean $\\frac{a \\cdot 15^2}{2} = \\frac{375}{2} (BB\u2019 = AA\u2019)$<\/p>\n

$\\Rightarrow a = \\frac{5}{3} \\Rightarrow v_B(t) = \\frac{5}{3}t$<\/p>\n

Khi \u0111u\u1ed5i k\u1ecbp A th\u00ec $t=15 \\Rightarrow v_B(15) = \\frac{5}{3} \\cdot 15 = 25 (m\/s)$<\/p>\n<\/div>\n

\n

C\u00c2U 2<\/p>\n

M\u1ed9t \u00f4 t\u00f4 \u0111ang chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c $v_0$ m\/s th\u00ec ng\u01b0\u1eddi l\u00e1i xe \u0111\u1ea1p phanh. T\u1eeb th\u1eddi \u0111i\u1ec3m \u0111\u00f3, \u00f4 t\u00f4 chuy\u1ec3n \u0111\u1ed9ng ch\u1eadm d\u1ea7n \u0111\u1ec1u v\u1edbi v\u1eadn t\u1ed1c thay \u0111\u1ed5i theo h\u00e0m s\u1ed1 $v(t) = -5t + 20$ m\/s, trong \u0111\u00f3 $t$ l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y k\u1ec3 t\u1eeb l\u00fac \u0111\u1ea1p phanh.<\/p>\n

a) $v_0 = 20m\/s$.b) Th\u1eddi gian t\u1eeb l\u00fac ng\u01b0\u1eddi l\u00e1i xe \u0111\u1ea1p phanh cho \u0111\u1ebfn khi xe d\u1eebng h\u1eb3n l\u00e0 5 gi\u00e2y.
\nc) $\\int (-5t + 20)dt = -\\frac{5t^2}{2} + 20t + C$.
\nd) Qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb l\u00fac \u0111\u1ea1p phanh cho \u0111\u1ebfn khi xe d\u1eebng h\u1eb3n l\u00e0 400 m.<\/p>\n

\u0110\u00e1p \u00e1n: \u0110\u00fang \u2013 Sai \u2013 \u0110\u00fang \u2013 Sai<\/p>\n

L\u1eddi gi\u1ea3i<\/p>\n

a) Khi $t = 0$ th\u00ec $v(0) = -5 \\cdot 0 + 20 = 20 (m\/s)$<\/p>\n

b) Khi xe d\u1eebng h\u1eb3n th\u00ec $v(t) = 0 \\Leftrightarrow -5t + 20 = 0 \\Rightarrow t = 4$<\/p>\n

c) $\\int (-5t + 20)dt = -\\frac{5t^2}{2} + 20t + C$<\/p>\n

d) Qu\u00e3ng \u0111\u01b0\u1eddng t\u1eeb l\u00fac \u0111\u1ea1p phanh ($t=0$) t\u1edbi l\u00fac d\u1eebng h\u1eb3n ($t=4$) l\u00e0:<\/p>\n

$S = \\int_0^4 (-5t + 20)dt = 40(m)$<\/p>\n<\/div>\n

V\u00e0 nhi\u1ec1u b\u00e0i to\u00e1n kh\u00e1c v\u1edbi \u0111\u1ed9 kh\u00f3 v\u00e0 d\u1ea1ng b\u00e0i kh\u00e1c nhau, bao ph\u1ee7 nhi\u1ec1u kh\u00eda c\u1ea1nh c\u1ee7a chuy\u1ec3n \u0111\u1ed9ng.<\/p>\n

T\u1ea3i 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi<\/h2>\n

\u0110\u00e2y l\u00e0 ngu\u1ed3n t\u00e0i li\u1ec7u v\u00f4 c\u00f9ng h\u1eefu \u00edch cho vi\u1ec7c \u00f4n t\u1eadp v\u00e0 chu\u1ea9n b\u1ecb cho c\u00e1c k\u1ef3 thi. \u0110\u1ec3 n\u00e2ng cao kh\u1ea3 n\u0103ng gi\u1ea3i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng, b\u1ea1n h\u00e3y t\u1ea3i file 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi \u0111\u1ec3 luy\u1ec7n t\u1eadp ngay nh\u00e9!<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

T\u1ea3i 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

T\u00e0i li\u1ec7u 20 b\u00e0i to\u00e1n chuy\u1ec3n \u0111\u1ed9ng th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong \u0111\u1ec1 thi ch\u1ee9a 20 b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a v\u1eadt th\u1ec3 ho\u1eb7c xe c\u1ed9. M\u1ed7i b\u00e0i to\u00e1n \u0111\u1ec1u c\u00f3 c\u00e2u h\u1ecfi v\u00e0 \u0111\u00e1p \u00e1n k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft. C\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn v\u1eadn t\u1ed1c, gia t\u1ed1c, qu\u00e3ng […]\n","protected":false},"author":1,"featured_media":1841,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[78,77,10],"class_list":["post-642","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-toan-12","tag-anh-giao-kid","tag-flash-study","tag-toan-12"],"_links":{"self":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=642"}],"version-history":[{"count":1,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/642\/revisions"}],"predecessor-version":[{"id":1842,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/642\/revisions\/1842"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/1841"}],"wp:attachment":[{"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/79.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}