Question

7. A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.7 shows graphs of $v_x$and $v_y$, the x-and y-components of the puck's velocity. The puck starts at the origin. What is the magnitude of the puck's acceleration at ?

Short answer

The magnitude of the acceleration is$2.2\text{m}/{\text{s}}^2$

Step-by-step solution

Step 1. Given information

The velocity in x-direction change from -10 m/s to 10 m/s in 5 second

The velocity in y-direction change from 0 m/s to 10 m/s in 10 second

Step 2. Explanation

The acceleration in x-direction is

$\begin{array}{l}{a}_x=\frac{d{v}_x}{dt}=\frac{\Delta v_x}{\Delta t}\\ =\frac{(-10\text{m}/\text{s}-10\text{m}/\text{s})}{10\text{s}-0\text{s}}\\ =-2.0\text{m}/{\text{s}}^2\end{array}$

The acceleration in y-direction is

$a_y=\frac{(10\text{m}/\text{s}-0\text{m}/\text{s})}{(10\text{s}-0\text{s})}=1.0\text{m}/{\text{s}}^2$

The magnitude of the acceleration is .

$a=\sqrt{a_x^2+a_y^2}=2.2\text{m}/{\text{s}}^2$