# Applied Physics: Displacement, Velocity and Acceleration

Work out the following problems. Be sure to show your work in detail.

1. A car is driving along a straight section of highway between Oklahoma City and Tulsa. At one point in time, the car is 50 miles from Tulsa. At a later point in time, it's 40 miles from Tulsa. What is its displacement?

2. An ant is placed on a piece of graph paper. It crawls 3 cm on an azimuth (course angle) of 30 degrees, 5 cm on an azimuth of 180 degrees, and 2 cm on an azimuth of 270 degrees. At that point, the observer loses patience and swats and ant. What is the X-Y position of the squashed ant, measured with respect of the place where it started?

3. A motorcycle rider is attempting to set a speed record on a straight course. The cycle passes two points, a measured 100 m apart, in 1.2 seconds. What is its average velocity between those points?

4. A M1911 pistol fires a .45 ACP round. The bullet leaves the 13 cm barrel with a velocity of 300 m/s.

a. What is the bullet's average velocity while in the barrel?

b. If the acceleration is assumed to be constant, how long does it take the bullet to travel the length of the barrel?

c. What is the average acceleration of the bullet in the barrel?

5. A small powder charge propels a shoulder-launched antitank missile from its tube at 20 m/s. At 0.2 seconds after launch, the rocket motor ignites and accelerates the missile at a constant 20 g. After 2 seconds, the missile hits its target and detonates. How far away was the target? Assume a straight flight path. (Hint: Calculate two distances, one before and one after rocket motor ignition.)

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#### Solution Preview

Displacement is the change in vector position, that is to say, it's simply the distance traveled, with a direction attached to it (a vector).

At point A, it was 50 miles from Tulsa, and at point B, it was 40 miles from Tulsa. This means it travelled 50-40=10 miles in total.

If we take point B, Tulsa, as our reference point, we can say that the car's displacement was 10 miles [towards Tulsa]. Alternatively, if point A, Oklahoma, was our reference point, it would be 10 miles [away from Oklahoma].

This second question might be easier to figure out if you draw out the question. Keep in mind, an azimuth starts off with the object facing 0 degrees "north", then goes clockwise with increasing angles (so facing "east" would be 90 degrees).

In the diagram attached, I've drawn out the ant's path, and the two distances we need to determine. Although not exactly ...

#### Solution Summary

Displacement, velocity and accelerations are examined for applied physics.