First slide

Motion in two and three dimensions

Question

Starting from the origin at time t = 0, with initial velocity $5 \hat{j} m s^{- 1}$ , a particle moves in the $x - y$ plane with a constant acceleration of $(10 \hat{i} + 4 \hat{j}) m s^{- 2}$ . At time t, its coordinates are $(20 m, y_{0} m)$ . The value of t and $y_{0}$ are, respectively :

Moderate

A

5 s and 25 m
B

2 s and 24 m
C

2 s and 18 m
D

4 s and 52 m

Solution

$\begin{array}{l} \bar{S} = t \bar{u} + \frac{1}{2} t^{2} \bar{a} \\ \Rightarrow 20 \hat{i} + y_{0} \hat{j} = t_{0} (5 \hat{j}) + \frac{1}{2} t_{0}^{2} (10 \hat{i} + 4 \hat{j}) \end{array}$
Equating components wise,
$\begin{array}{l} 20 = 5 t_{0}^{2} \\ \Rightarrow t_{0} = 2 \sec \\ a n d \\ y_{0} = 5 t_{0} + 2 t_{0}^{2} \\ \Rightarrow y_{0} = 18 m \end{array}$

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