The x and y coordinates of the particle at any time are x = 5 t - 2 t 2 and y = 10 t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 ? s is [2017]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The $x$ and $y$ coordinates of the particle at any time are $x = 5 t - 2 t^{2}$ and $y = 10 t$ respectively, where $x$ and $y$ are in metres and $t$ in seconds. The acceleration of the particle at $t = 2 s$ is [2017]

1 $5 {ms}^{- 2}$

2 $- 4 {ms}^{- 2}$

3 $- 8 {ms}^{- 2}$

4 $0$

Ans.
(2)

$x = 5 t - 2 t^{2}, y = 10 t$

$\frac{d x}{d t} = 5 - 4 t, \frac{d y}{d t} = 10 ∴$ $v_{x} = 5 - 4 t, v_{y} = 10$

$\frac{d v_{x}}{d t} = - 4, \frac{d v_{y}}{d t} = 0 ∴$ $a_{x} = - 4, a_{y} = 0$

$Acceleration, \vec{a} = a_{x} \hat{i} + a_{y} \hat{j} = - 4 \hat{i}$

$∴$ $The acceleration of the particle at t = 2 s is - 4 {ms}^{- 2} .$

Want Us to Email you About Special Offers & Updates?