Question

a 450 - kg sports car accelerates from rest to 100 km/h in 4.80 s. what magnitude force does a 68.0 kg passenger experience during the acceleration?
a) 342 n
b) 184 n
c) 362 n
d) 284 n
e) 394 n
f) 311 n

Explanation:

Step1: Convert velocity unit

Convert \(100\ km/h\) to \(m/s\).
\(v = 100\times\frac{1000}{3600}\ m/s=\frac{250}{9}\ m/s\approx27.78\ m/s\)

Step2: Calculate acceleration

Use the formula \(a=\frac{v - u}{t}\), where \(u = 0\ m/s\) (starts from rest), \(v\) is the final velocity and \(t\) is the time.
\(a=\frac{\frac{250}{9}-0}{4.80}=\frac{250}{9\times4.80}\ m/s^{2}\approx5.79\ m/s^{2}\)

Step3: Calculate force on passenger

Use Newton's second law \(F = ma\), where \(m = 68.0\ kg\) is the mass of the passenger and \(a\) is the acceleration.
\(F=68.0\times\frac{250}{9\times4.80}=68.0\times5.79\ N\approx394\ N\)

Answer:

e) \(394\ N\)