Kinematics in One Dimension (Concept Test)

2.1 Walking the dog

You and your dog go for a walk to the park.  On the way, your dog takes many side trips to chase squirrels or examine fire hydrants.  When you arrive at the park, do you and your dog have the same displacement?

• Yes

• No

Answer explanation

Yes, you have the same displacement.  Since you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement. 

2.2 Displacement

Does the displacement of an object depend on the specific location of the origin of the coordinate system?

• yes

• no

• it depends on the coordinate system

Answer explanation

Since the displacement is the difference between two coordinates, the origin does not matter.

2.3 Position and Speed

If the position of a car is zero, does its speed have to be zero?

• yes

• no

• it depends on the position

Answer explanation

No, the speed does not depend on position, it depends on the change of position.  Since we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = –3 and be moving by the time it gets to x = 0. 

2.4 Odometer

Does the odometer in a car measure distance or displacement?

• distance

• displacement

• both

Answer explanation

If you go on a long trip and then return home, your odometer does not measure zero, but it records the total miles that you travelled.   That means the odometer records distance.

2.5 Speedometer

Does the speedometer in a car measure velocity or speed?

• velocity

• speed

• both

• neither

Answer explanation

The speedometer clearly measures speed, not velocity.  Velocity is a vector (depends on direction), but the speedometer does not care what direction you are traveling.  It only measures the magnitude of the velocity, which is the speed.

2.6a Cruising Along I

You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. What is your average speed for the whole trip?

• more than 40 mi/hr
• equal to 40 mi/hr
• less than 40 mi/hr

Answer explanation

It is 40 mi/hr in this case. Since the average speed is distance/time and you spend the same amount of time at each speed, then your average speed would indeed be 40 mi/hr.

2.6b Cruising Along II

You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip?

• more than 40 mi/hr
• equal to 40 mi/hr
• less than 40 mi/hr

Answer explanation

It is not 40 mi/hr! Remember that the average speed is distance/time. Since it takes longer to cover 4 miles at the slower speed, you are actually moving at 30 mi/hr for a longer period of time! Therefore, your average speed is closer to 30 mi/hr than it is to 50 mi/hr.

2.7 Velocity in One Dimension

If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval?

• yes
• no
• it depends

Answer explanation

No!!! For example, your average velocity for a trip home might be 60 mph, but if you stopped for lunch on the way home, there was an interval when your instantaneous velocity was zero, in fact!

2.8a Acceleration I

If the velocity of a car is non-zero (v ¬π 0), can the acceleration of the car be zero?

• yes
• no
• depends on the velocity

Answer explanation

Sure it can! An object moving with constant velocity has a non-zero velocity, but it has zero acceleration since the velocity is not changing.

2.8b Acceleration II

When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path?

• both v = 0 and a = 0
• v ≠ 0, but a = 0
• v = 0, but a ≠ 0
• both v ≠ 0 and a ≠ 0
• not really sure

Answer explanation

At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise it would remain at rest!!