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Chapter 2: Problem 28

You're driving at \(70 \mathrm{km} / \mathrm{h}\) when you apply constant acceleration to pass another car. Six seconds later, you're doing \(80 \mathrm{km} / \mathrm{h}\). How far did you go in this time?

Short Answer

Expert verified
The distance travelled while passing the other car can be found by solving \(d = v_i\Delta t + 0.5 a (\Delta t)^2\) where \( v_i, a , \Delta t \) are known.

Step by step solution

01

Determine the acceleration

The acceleration during the maneuver can be found from the difference in velocities and the time taken. The formula to calculate acceleration is \(a = \frac{\Delta v}{\Delta t}\) where, \(\Delta v = v_f - v_i\) is the change in velocity. Given that the initial velocity \(v_i\) is 70 km/h, the final velocity \(v_f\) is 80 km/h, and the time \(\Delta t\) is 6 seconds. Be aware to convert the velocities from km/h to m/s by multiplying by \( \frac{5}{18} \). So, \( \Delta v = \frac{5}{18} * (80-70) \) and the acceleration \( a = \frac{\Delta v}{\Delta t}\).
02

Calculate the distance travelled

The distance \(d\) traveled under acceleration is given by the equation \(d = v_i\Delta t + 0.5 a (\Delta t)^2\). Substitute the values of \( v_i, a , \Delta t \) into this equation to find the distance travelled. Remember to convert \(v_i\) from km/h to m/s by multiplying by \( \frac{5}{18} \).

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