Example Solutions

1. Does a car speedometer measure speed, velocity, or both?

 

Speed is a scalar quantity that tells us how fast an object is traveling only. It does not tell us the direction the object is moving.

Velocity is a vector quantity that tells us the direction an object is going and how fast it's traveling.

Since a car speedometer only tells us how fast the car is going and not the direction it only measures speed.

 

2. Can an object have a varying speed if its velocity is constant? If yes, give examples

 

No, an object cannot have varying speed if its velocity is constant.

We know that the velocity of a moving object is defined by its speed as well as direction. When the velocity is constant, it means that both the speed and the direction are constant. Therefore, speed cannot vary when velocity is constant.

 

3. When an object moves with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant?

 

No, the average velocity of an object during any time interval does not differ from its instantaneous velocity at any instant, as long as the object moves with constant velocity.

 

We know that the instantaneous velocity at any moment is defined as the average velocity when the time interval is too small. So, when the velocity remains constant, the average velocity and the instantaneous velocity remain equal.

4. Omit

 

5.  Can an object have a northward velocity and a southward acceleration? Explain.

 

Yes. When a car heading north is braking, it has a northward velocity but it is slowing down, so it has an acceleration in the opposite direction, i.e. a southward acceleration.

 

6.  Give an example where both the velocity and acceleration are negative.

Assume the the positive direction is up

You can throw a stone straight up, when it eventually comes down its velocity points downward, thus is negative; and its acceleration,  9.8 m/s², also negative.

7.  As a freely falling object speeds up, what is happening to its acceleration due to gravity — does it increase, decrease, or stay the same?

 

For any free-falling object, its acceleration stays constant at 9.8 m/s². It does not matter whether the object is going up or down, whether the object is speeding up or slowing down.

 

8.  Can an object have zero velocity and nonzero acceleration at the same time? Give examples.

 

An object can have zero velocity and nonzero acceleration at the same time.

 

Consider a ball thrown upwards. At the maximum height, velocity becomes zero for an instant. But, it will experience acceleration downwards due to gravity. If the acceleration were zero, the velocity would remain zero at the highest point, and the ball would stay up there without falling.

 

Same is in the case of a simple pendulum. At the point of maximum displacement, the velocity will become momentarily zero. But, the acceleration will have a positive value equal to the acceleration due to gravity.