# Second Law of Motion

(1)

In three dimensions, we write what is often called Newtonâ€™s second law:

(3a)

(3b)

Bruce pushes a car (500 kg) on level ground starting from rest with a force 100 N. How long does it take to get the car rolling 1 m/s? (Assume no friction.)

We have the information *m* = 500 kg, *v*_{1} = 0 m/s, *F* = 100 N, and *v*_{2} = 1 m/s, and we want Î”*t*. We can find acceleration from equation (1), so we obtain

Then we can find Î”*t* from

A rocket provides a constant force to wagon A that rolls without friction. It starts from rest and after time t attains velocity v. A similar rocket providing the same force is attached to wagon B, which has five times the mass of A (Figure 3-7). How much time does it take wagon B to go from rest to velocity v? (Assume no friction.)

This one looks difficult, but if we write down the relevant equations, it is not so hard. We need to connect force and velocity, so we write,

We set *v*_{1} to zero because the wagons start from rest. Substitution gives

Since the problem asks about the change in time, we can solve for Î”*t* to obtain

Now, *F* and *v*_{2} stay the same, but m is five times larger for wagon B, so Î”*t* is five times larger.

The answer is 5*t*.