Answer to Question #95281 in Mechanics | Relativity for Paola Garcia

Question

A car waits at a red light for a few seconds, and then accelerates straight ahead to 54 km/h in 3.1 s and then cruises at a constant speed for 75 m. The road is straight. Find the total distance and time travelled.

Answer 1

$$S = S_{a} + S_{cs}= S_{a} +75$$

$$S_{a}=V_{0}\times t_{a} +\frac{a\times t_{a}^2}{2}$$ $$S_{a}=V_{0}\times t_{a} +\frac{(V-V_{0})\times t_{a}}{2}$$

Where V₀=0, t_a= 3.1 s, V = 54 km/h= 15 m/s

$$S_{a}= \frac{15\times3.1}{2}= 23.25 m$$

$$S =23.25 +75= 98.25 m$$

$$t= t_{a}+t_{cs}$$

$$t_{cs}= \frac{S_{cs}}{V}= \frac{75}{15}= 5 s$$

$$t= 3.1+5=8.1 s$$