1. ## More Forces

An advertisement claims that a particular automobile can "stop on a dime". What net force would actually be necessary to stop an automobile of mass 940 kg traveling initially at a speed of 38.0 km/h in a distance equal to the diameter of a dime, which is 1.8 cm?

I'm not even sure how to begin with this. Maybe if I can find an appropriate acceleration, I can find the force needed to do this?

2. Let F = force to stop the car.

Then, F = ma
F = 940*a ----------------(1)

What is "a"?
It is deceleration, of course.

Given:
Initial velocity, Vo = 38km/hr = (38km/1hr)(1000m/1km)(1hr/3600sec) = 10.555.... m/sec
Final velocity, Vt = 0
Distance travelled, s = 1.8 cm = (1.8cm)(1m/100cm) = 0.018 m

Distance = (average velocity) * time
s = (1/2)(Vo +Vt)*t
0.018 = (1/2)(10.555... +0)*t
t = 0.018 / (10.555... /2) = 0.00341 sec.

Velocity at t = (initial velocity) + a*t
Vt = Vo +at
0 = 10.555... +a(0.00341)
a = -10.555... /0.00341 = -3095.47 m/sec/sec

Hence,
F = ma
F = 940(-3095.47) = -2,909,742 newtons <---almost 3 million newtons!

Negative, because F is against the direction of the car.

3. I think I get it.

I'll go over it again and let you know if I have any problems.

Thanks!