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(a) Can an object have zero velocity and still be accelerating? (b) Can an object have a constant velocity and still have a varying speed? In each case, give an example if your answer is yes; explain why if your answer is no.

(a) Can an object have zero velocity and still be accelerating?
(b) Can an object have a constant velocity and still have a varying speed? In each case, give an example if your answer is yes; explain why if your answer is no.

Grade:11

5 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
(a) Yes, an object can have zero velocity and still be accelerating simultaneously.
Consider an object moving in the forward direction. Suddenly a force acts on it and tries to accelerate the object in the backward direction. When you observe the object, you will find that the object will continue to move forward for some time and then stops momentarily. Then the object will start to move in the backward direction.
When the object stops for a moment, its velocity at that instant is zero, therefore no motion in either forward or backward direction. However the acceleration is still acting on it. At that instant, the magnitude of velocity in the backward direction is equal to the velocity in the forward direction, but as the acceleration continues to act on it, the velocity in the backward direction increases in magnitude over time, and the object finally starts moving in the backward direction.
One can also see this mathematically. For example consider that the velocity of any object at any time t is given as:
v (t) = t -2.
The acceleration of the object is:
a (t) = 1
However at 1 = 2 the velocity v(t) of the object is zero but the acceleration is still constant i.e. 1.
(b) Yes, an object can have a constant velocity and still have a varying speed.
For example, consider that a car moves from point A to point B by traversing a distance of 30 km in 1 hour. However the magnitude of displacement vector between the two points is 10 km.
The car then travels to point C by traversing a distance of 20 km in 1 hour. The magnitude of displacement vector between points B and C is the same i.e.10 km.
Therefore the magnitude of velocity of the car when it moves from point A to point B and from point B to C is
velocity = \frac{displacement}{time}
= \frac{10\ km}{1\ h}
= 10\ km/\ h
However the speed (say speed AB )of the car when it moves from point A to B is:
speed _{AB} = \frac{distance}{time}
= \frac{30\ km}{1\ h}
= 30\ km /\ h
The speed (say speedAB ) of the car when it moves from point B to C is:
speed_{BC} = \frac{distance}{time}
= \frac{20\ km}{1\ h}
= 20\ km/\ h
Therefore we find that the speed of the car is different when it moves from point A to point B relative to when it moves from point B to point C, however the magnitude of velocity is remains the same.
Bintte Javaid
26 Points
7 years ago
when velocity is constant  evrage velocity overthe time interval differ from any   instntanious velocity at any instant ?
Tathwam Roy
19 Points
6 years ago
Yes for eg consider that a body is thrown vertically up.At the highest pt the body posseses zero velocity and finite acceleration
Deepraj
11 Points
6 years ago
Therefore we find that the speed of the car is different when it moves from point A to point B relative to when it moves from point B to point C, however the magnitude of velocity is remains the same.= 20\ km/\ h= \frac{20\ km}{1\ h}speed_{BC} = \frac{distance}{time} ) of the car when it moves from point B to C is:ABThe speed (say speed= 30\ km /\ h= \frac{30\ km}{1\ h}speed _{AB} = \frac{distance}{time} )of the car when it moves from point A to B is:ABHowever the speed (say speed = 10\ km/\ h= \frac{10\ km}{1\ h}velocity = \frac{displacement}{time}(a) Yes, an object can have zero velocity and still be accelerating simultaneously.Consider an object moving in the forward direction. Suddenly a force acts on it and tries to accelerate the object in the backward direction. When you observe the object, you will find that the object will continue to move forward for some time and then stops momentarily. Then the object will start to move in the backward direction.When the object stops for a moment, its velocity at that instant is zero, therefore no motion in either forward or backward direction. However the acceleration is still acting on it. At that instant, the magnitude of velocity in the backward direction is equal to the velocity in the forward direction, but as the acceleration continues to act on it, the velocity in the backward direction increases in magnitude over time, and the object finally starts moving in the backward direction.One can also see this mathematically. For example consider that the velocity of any object at any time t is given as:v (t) = t -2.The acceleration of the object is:a (t) = 1However at 1 = 2 the velocity v(t) of the object is zero but the acceleration is still constant i.e. 1.(b) Yes, an object can have a constant velocity and still have a varying speed.For example, consider that a car moves from point A to point B by traversing a distance of 30 km in 1 hour. However the magnitude of displacement vector between the two points is 10 km.The car then travels to point C by traversing a distance of 20 km in 1 hour. The magnitude of displacement vector between points B and C is the same i.e.10 km.Therefore the magnitude of velocity of the car when it moves from point A to point B and from point B to C is
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

(a) Yes, an object can have zero velocity and still be accelerating simultaneously. Consider an object moving in the forward direction. Suddenly a force acts on it and tries to accelerate the object in the backward direction. When you observe the object, you will find that the object will continue to move forward for some time and then stops momentarily. Then the object will start to move in the backward direction. When the object stops for a moment, its velocity at that instant is zero, therefore no motion in either forward or backward direction. However the acceleration is still acting on it. At that instant, the magnitude of velocity in the backward direction is equal to the velocity in the forward direction, but as the acceleration continues to act on it, the velocity in the backward direction increases in magnitude over time, and the object finally starts moving in the backward direction. One can also see this mathematically. For example consider that the velocity of any object at any time t is given as: v (t) = t -2. The acceleration of the object is: a (t) = 1 However at 1 = 2 the velocity v(t) of the object is zero but the acceleration is still constant i.e. 1. (b) Yes, an object can have a constant velocity and still have a varying speed. For example, consider that a car moves from point A to point B by traversing a distance of 30 km in 1 hour. However the magnitude of displacement vector between the two points is 10 km. The car then travels to point C by traversing a distance of 20 km in 1 hour. The magnitude of displacement vector between points B and C is the same i.e.10 km. Therefore the magnitude of velocity of the car when it moves from point A to point B and from point B to C is
velocity = displacement/time
= 10 km/1h
= 10 km/h
However the speed (say speed AB )of the car when it moves from point A to B is: speed{AB} = distance/time
= 30 km/1 h
= 30 km/h
The speed (say speedAB ) of the car when it moves from point B to C is:
speed_{BC} = distance/time
= 20km/1h
= 20km/h
Therefore we find that the speed of the car is different when it moves from point A to point B relative to when it moves from point B to point C, however the magnitude of velocity is remains the same

Thanks and Regards

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