Chapter 3, Problem 3STP

To determine

To Choose: The correct option.

Answer to Problem 3STP

Option A: $0.44{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Initial velocity of the car, $u=80\text{km/h}$

Final velocity of the car, $v=110\text{km/h}$

Displacement of the car, $s=500\text{m}$

Formula Used:

Third equation of motion:

  $2as=v^2-u^2$

Where, s is the displacement, u is the initial velocity,v is the final velocity and a is the acceleration.

Calculations:

First, convert velocity from km/h to m/s.

  $\begin{array}{c}u=80\text{km/h}\\ \text{=80}\times \frac{1000}{3600}\text{m/s}\\ \text{=22}\text{.22}\text{m/s}\end{array}$

  $\begin{array}{c}v=110\text{km/h}\\ \text{=110}\times \frac{1000}{3600}\text{m/s}\\ \text{=30}\text{.56}\text{m/s}\end{array}$

Now, re-arrange the formula and substitute the values to solve:

  $\begin{array}{c}2as=v^2-u^2\\ a=\frac{v^2-u^2}{2s}\\ a=\frac{{30.56}^2-{22.22}^2}{2\times 500}\\ a=0.44{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Thus, correct option is A.