Acceleration 7054

The car brakes with an acceleration of 5 m/s-2. Determine the stopping distance of the car if its initial speed is

a) 54 km/h,
b) 108 km/h.

Compare the calculated braking distances concerning the given speeds.

Correct answer:

a =  22.5 m
b =  90 m

Step-by-step explanation:

$$\begin{gathered} v_1=54\text{km/h}\to \text{m/s}=54:3.6\text{m/s}=15\text{m/s} \\ z=5{\text{m/s}}^2 \\ {t}_1=v_1/z=15/5=3\text{s} \\ a=\frac{1}{2}\cdot z\cdot t_1^2=\frac{1}{2}\cdot 5\cdot 3^2=\frac{45}{2}\text{m}=22.5\text{m} \end{gathered}$$

$$\begin{gathered} v_2=108\text{km/h}\to \text{m/s}=108:3.6\text{m/s}=30\text{m/s} \\ {t}_2=v_2/z=30/5=6\text{s} \\ b=\frac{1}{2}\cdot z\cdot t_2^2=\frac{1}{2}\cdot 5\cdot 6^2=90=90\text{m} \\ {c}_1=v_2/v_1=30/15=2 \\ {c}_2=b/a=90/\frac{45}{2}=90:\frac{45}{2}=90\cdot \frac{2}{45}=\frac{90\cdot 2}{45}=\frac{180}{45}=4 \end{gathered}$$

Try another example