First slide

Motion in a plane

Question

A particle starts from the origin at t = 0 s with a velocity of $10.0 \hat{j} m / s$ and moves in the xy-plane with a constant acceleration of $8.0 \hat{i} + 2.0 \hat{j} {ms}^{- 2}$ . At what time is the x-coordinate of the particle 16 m?

Moderate

A

t = 2s
B

t = 4s
C

t = 3s
D

t = 1s

Solution

$\large \overline S = \overline u t + \frac{1}{2}\overline a {t^2} \Rightarrow {S_x}\hat i + {S_y}\hat j = (10\widehat j)t + \frac{1}{2}(8\widehat i + 2\widehat j){t^2}$
$\large \Rightarrow {S_x} = 4{t^2} = 16 \Rightarrow$ $\large t^2=4\Rightarrow t=2s$

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