Chapter 4, Problem 1WUE

Physics Review A hockey player strikes a puck, giving it an initial velocity of 10.0 m/s in the positive x-direction. The puck slows uniformly to 6.00 m/s when it has traveled 40.0 m. (a) What is the puck’s acceleration? (b) At what velocity is it traveling after 2.00 s? (c) How long does it take to travel 40.0 m? (See Section 2.5.)

To determine

The puck acceleration.

Answer to Problem 1WUE

Solution:

The acceleration of puck is $-0.80{\text{m}/\text{s}}^2$.

Explanation of Solution

Given Info:

The initial velocity of puck is $10.0\text{m}/\text{s}$, final velocity of the puck is $6.00\text{m}/\text{s}$ and the distance travelled by the puck is $40.0\text{m}$.

Write the formula to calculate the acceleration on the puck.

$a=\frac{v^2-v_o{}^2}{2\Delta x}$

• a is the acceleration on the puck
• v is the final velocity of the puck
• $v_o$ is the initial velocity of the puck
• $\Delta x$ is the distance or displacement of puck

Substitute $6.00\text{m}/\text{s}$ for v, $10.0\text{m}/\text{s}$ for $v_o$, and $40.0\text{m}$ for $\Delta x$ to calculate a,

$\begin{array}{c}a=\frac{{\left(6.00\text{m}/\text{s}\right)}^2-{\left(10.0\text{m}/\text{s}\right)}^2}{2\left(40.0\text{m}\right)}\\ =-\frac{64{{\text{m}}^2/\text{s}}^2}{80\text{m}}\\ =-0.80{\text{m}/\text{s}}^2\end{array}$

Conclusion:

Therefore, the acceleration of puck is $-0.80{\text{m}/\text{s}}^2$

To determine

The velocity of puck after $2.00\text{s}$.

Answer to Problem 1WUE

Solution:

The velocity of the puck after $2.00\text{s}$ is $8.4\text{m}/\text{s}$.

Explanation of Solution

Given Info:

The acceleration of the puck is $-0.80{\text{m}/\text{s}}^2$.

Write the formula to calculate the velocity.

$v=v_o+at$

• t is the time taken by the puck.

Substitute $10.0\text{m}/\text{s}$ for $v_o$, $2.00\text{s}$ for t and $-0.80{\text{m}/\text{s}}^2$ for a to calculate v.

$\begin{array}{c}v=10.0\text{m}/\text{s}+\left(-0.80{\text{m}/\text{s}}^2\right)\left(2.00\text{s}\right)\\ =10.0\text{m}/\text{s}-1.60\text{m}/\text{s}\\ =8.4\text{m}/\text{s}\end{array}$

Conclusion:

Therefore, the velocity of the puck after $2.00\text{s}$ is $8.4\text{m}/\text{s}$.

To determine

The time required to travel $40.0\text{m}$.

Answer to Problem 1WUE

Solution:

The time required to travel $40.0\text{m}$ is $5.00\text{s}$.

Explanation of Solution

Given Info:

The initial velocity of puck is $10.0\text{m}/\text{s}$, final velocity of the puck is $6.00\text{m}/\text{s}$ and the acceleration of the puck is $-0.80{\text{m}/\text{s}}^2$.

Write the formula to calculate the time.

$t=\frac{v-v_o}{a}$

Substitute $10.0\text{m}/\text{s}$ for $v_o$ $6.00\text{m}/\text{s}$ for v, and $-0.80{\text{m}/\text{s}}^2$ for a to calculate t.

$\begin{array}{c}t=\frac{6.00\text{m}/\text{s}-10.0\text{m}/\text{s}}{-0.80{\text{m}/\text{s}}^2}\\ =\frac{-4.00\text{m}/\text{s}}{-0.80{\text{m}/\text{s}}^2}\\ =5.00\text{s}\end{array}$

Conclusion:

Therefore, the time required to travel $40.0\text{m}$ is $5.00\text{s}$