First slide

Motion in two and three dimensions

Question

A particle starts from the origin at $t = 0$ with an initial velocity of $3.0 \hat{i} m / s$ and moves in the $x - y$ plane with a constant acceleration $(6.0 \hat{i} + 4.0 \hat{j}) m / s^{2}$ . The $x$ -coordinate of the particle at the instant when its y–coordinate is 32m is ________ meters.

Moderate

A

50
B

32
C

60
D

40

Solution

$\begin{array}{l} G i v e n : u_{x} = 3 m / s, a_{x} = 6 m / s^{2}, a_{y} = 4 m / s^{2} \\ B y a p p l y i n g e q u a t i o n s o f K i n e m a t i c s : \\ y = u_{y} t + \frac{1}{2} a_{y} t^{2} \\ \Rightarrow 32 = 0 + \frac{1}{2} \times 4 \times t^{2} \\ \Rightarrow t^{2} = 16 \\ \Rightarrow t = 4 s \\ N o w, x = u_{x} t + \frac{1}{2} a_{x} t^{2} \\ \Rightarrow x = 3 \times 4 + \frac{1}{2} \times 6 \times 16 \\ \Rightarrow x = 12 + 48 = 60 m \end{array}$

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