Chapter 3.2, Problem 25PP

To determine

To Calculate: The time taken by the car to achieve the final speed.

Answer to Problem 25PP

  $6.25\text{s}$

Explanation of Solution

Given:

The given car accelerates at a constant rate of $\text{15 m/s to 25 m/s}$ and travels a distance of 125m.

Formula used:

Final velocity with constant acceleration can be obtained by:

  $v_{final}=v_{initial}+a\Delta t$

Where, $\Delta t$ is the time taken, a is acceleration and v represents velocity.

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 displacement, v represents velocity, t represents time and a is the acceleration.

Calculation:

It is given that the initial velocity of the car is $15\text{m/s}$ while the final velocity is $25\text{m/s}$ . Thus, it can be written as

  $\begin{array}{c}{v}_{final}=v_{initial}+a\Delta t\\ 25=15+a\Delta t\\ a=\frac{10}{\Delta t}\mathrm{..........}\left(1\right)\end{array}$

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

  $\begin{array}{c}{d}_{final}=d_{initial}+v_{initial}\Delta t+\frac{1}{2}a{\left(\Delta t\right)}^2\\ 125=0+15\Delta t+\frac{1}{2}\left(\frac{10}{\Delta t}\right){\left(\Delta t\right)}^2\\ 125=15\Delta t+5\Delta t\\ \Delta t=\frac{125}{20}\\ =6.25\text{s}\end{array}$

Conclusion:

Thus, time taken by the car is $6.25\text{s}$ .