Physics

Problem

t=0\,\text{s}

, a particle is located at the point

(2.0\,\text{m},\,1.0\,\text{m})

and has a velocity of

(1.0\,\text{m/s},\,-0.50\,\text{m/s})

. Four seconds later, the particle is at

(10.0\,\text{m},\,5.0\,\text{m})

. If the acceleration is constant, determine the

x

- and

y

-components of the particle’s average acceleration vector. Express each component with the correct units.

Intuitive explanation

The key is recognizing that constant acceleration means you can use the kinematic displacement equation to find how velocity must have changed. Calculate the displacement in each direction, then use $\Delta x = v_0 \Delta t + \frac{1}{2}a(\Delta t)^2$ to solve for the acceleration components separately—treating $x$ and $y$ motion independently. This is a straightforward application of constant-acceleration kinematics in two dimensions.

Intuitive explanation

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