To determine the mass of a car, a student (with a friend at the wheel) pushes the car holding a bathroom scale between himself and the car and carefully maintains a constant reading of 400 N on the scale while the car accelerates on level ground. At the conclusion of the experiment his friend reports that the car accelerated from rest to 14.0 km/hr in 12.0 s. What was the mass of the car?
A) 343 kg
B) 1230 kg
C) 2460 kg
D) 3360 kg
E) 3430 kg

Question

Quizplus · Accepted Answer

The force exerted by the student is 400 N. The acceleration can be calculated using the formula $ a = \frac{\Delta v}{\Delta t} $, where $ \Delta v = 14.0 \, \text{km/hr} = \frac{14.0 \times 1000}{3600} \, \text{m/s} \approx 3.89 \, \text{m/s} $ and $ \Delta t = 12.0 \, \text{s} $. Thus, $ a \approx \frac{3.89}{12} \approx 0.324 \, \text{m/s}^2 $. Using Newton's second law $ F = ma $, the mass $ m = \frac{F}{a} = \frac{400}{0.324} \approx 1230 \, \text{kg} $.

To Determine the Mass of a Car, a Student (With