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Of the following situations, which one is impossible? (a) A body having velocity east and acceleration east; (b) a body having velocity east and acceleration west; (c) a body having zero velocity but acceleration not zero; (d) a body having constant acceleration and variable velocity; (e) a body having constant velocity and variable acceleration.

Of the following situations, which one is impossible? (a) A body having velocity east and acceleration east; (b) a body having velocity east and acceleration west; (c) a body having zero velocity but acceleration not zero; (d) a body having constant acceleration and variable velocity; (e) a body having constant velocity and variable acceleration.

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Out of the following situations, situation (e) is impossible i.e. a body cannot have a constant velocity together with a variable acceleration.
The examples of all the situations are given below:
(a) Consider an object moving eastward such that its velocity changes from 10 km/h to 20 km/h in 1 sec. One can easily see that the acceleration vector in this case points in the direction of motion, which is eastwards. However, this is true as long as the object moves in a straight line.
(b) Consider a car moving eastward with velocity 20 km/h. The driver suddenly applies the brakes, such that the car starts to slow down. In this situation, the acceleration on the car, when the driver has applied the brakes is westwards thereby accounting for a smaller final velocity of the car.
(c)Consider the motion of a ball thrown vertically upward. The balls moves with some initial velocity, converts the given energy to the potential energy and rise to some height. When the ball reaches its maximum height, the velocity of the ball is zero. However the acceleration stills acts on it, which in this case is the acceleration due to gravity.
(d) Consider the motion of an object such that the velocity of the objects increases by a factor each second during its motion. The linear relationship between the velocity and time of the object highlights that the change of the velocity will always be constant and will be equal to the value of factor.
Suppose that object moves eastward from 5 m/s to 10 m/s in to . Then the objects moves to 15 m/s in the next second. Therefore the acceleration of the object when it moves from 5 m/s to 10 m/s is given as:
a = \frac{10\ m/\ s\ eastwards - m/\ s\ eastwards}{1s}
= 5\ m/\ s^{2} eastwards
And the acceleration of the object when it moves from 10 m/s to 15 m/s is:
a = \frac{15\ m/s eastwards-10m/\ s eastwards}{(2\ s-1\ s)}
= 5\ m/\ s^{2} eastwards
Therefore the acceleration of the object is constant while the velocity is variable.
(e)A body cannot have a constant velocity and the variable acceleration. This can be seen from the definition of the acceleration, defined as the rate of change of velocity over time. In case the velocity remained constant, neither its magnitude nor the direction changes thereby accounting for zero acceleration.
Haseeb
15 Points
one year ago
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