Chapter 3.2, Problem 27PP

To determine

To Calculate: The initial car velocity $\left(v_i\right)$ if it travels at a constant acceleration.

Answer to Problem 27PP

  $16.99\text{m/s}$

Explanation of Solution

Given:

The car travels with a constant acceleration of $0.22{\text{m/s}}^{\text{2}}$ and covers a distance of $350\text{ m}$ in $\text{18}\text{.4 s}$ .

Formula used:

The distance traveled by an object with a constant acceleration can be obtained by:

  $d_{final}=d_{initial}+v_{initial}\Delta t+\frac{1}{2}a\Delta t^2$

Here, d represents distance, v represents velocity, t represents time and a is the acceleration.

Calculation:

Assume that the initial position of the car is 0, that is $d_{initial}=0\text{m}$

Substitute the values in formula and solve:

  $\begin{array}{c}350=0+v_i\left(18.4\right)+\frac{1}{2}\left(0.22\right){\left(18.4\right)}^2\\ 350=18.4v_i+37.24\\ v_i=16.9\text{9}\text{m/s}\end{array}$

Conclusion:

Thus, the initial velocity of the car is $16.99\text{m/s}$ .