Question

a mercedes car can accelerate up to 200 km/h from rest in 10.9 seconds. how far has it gone in this time and what is its acceleration (in m/s²)?

distance = 1211 m, acceleration = 10.2 m/s²

distance = 605 m, acceleration = 9.17 m/s²

distance = 303 m, acceleration = 5.10 m/s²

distance = 303 m, acceleration = 10.2 m/s²

Explanation:

Step1: Convert velocity unit

Given \(v = 200\space km/h\), convert to \(m/s\): \(v=\frac{200\times1000}{3600}\space m/s\approx55.56\space m/s\), initial velocity \(u = 0\space m/s\), time \(t = 10.9\space s\)

Step2: Calculate acceleration

Using \(a=\frac{v - u}{t}\), substitute \(u = 0\), \(v\approx55.56\space m/s\), \(t = 10.9\space s\)
\(a=\frac{55.56- 0}{10.9}\space m/s^{2}\approx5.10\space m/s^{2}\)

Step3: Calculate distance

Using \(s=ut+\frac{1}{2}at^{2}\), substitute \(u = 0\), \(a\approx5.10\space m/s^{2}\), \(t = 10.9\space s\)
\(s=0\times t+\frac{1}{2}\times5.10\times(10.9)^{2}\)
\(s = 2.55\times118.81\space m\approx303\space m\)

Answer:

Distance = 303 m, Acceleration = 5.10 \(m/s^{2}\) (corresponds to the third option: Distance = 303 m, Acceleration = 5.10 \(m/s^{2}\))