First slide

Motion in a plane

Question

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

Moderate

A

$5 m s^{- 2}$
B

$- 4 m s^{- 2}$
C

$- 8 m s^{- 2}$
D

0

Solution

$x = 5 t - 2 t^{2}, y = 10 t$
$\frac{d x}{d t} = 5 - 4 t, \frac{d y}{d t} = 10 ∴ v_{x} = 5 - 4 t, v_{y} = 10$
$\frac{d v_{x}}{d t} = - 4, \frac{d v_{y}}{d t} = 0 ∴ a_{x} = - 4, a_{y} = 0$
$Acceleration, \vec{a} = a_{x} \hat{i} + a_{y} \hat{j} = - 4 \hat{i}$
$∴ The acceleration of the particle at t = 2 s is - 4 {ms}^{- 2}$

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