Question

State which of the following situations are possible and give an example for each of these:
(a) An object with a constant acceleration but with zero velocity
(b) An object moving in a certain direction with an acceleration in the perpendicular direction.

Answer 1

Hint
To check the validity of the statements given to us, we should come up with at least one example where we have seen an object with a constant acceleration but with a zero velocity. If we can’t find any examples, it will mean that the statement is not possible. Similarly, we will proceed with the second statement and check its validity.

Complete step by step answer
When we throw a body at a certain angle with the horizontal, we call it a projectile motion. In the projectile motion, the vertical component of the velocity keeps on changing whereas the horizontal component of the velocity remains constant throughout. Since we know that a force or a velocity is required for the variation in velocity. The acceleration acting on the body is the acceleration due to gravity, which as we know, has a constant value. Instead of this constant acceleration acting on the body, the horizontal component does not change.
Therefore the situation mentioned in statement (a) is possible.
Coming to the second situation, we know that when a body moves in a circular path, it exhibits what we call a circular motion. In a circular motion, a force called the centripetal force acts on the particle at every point along the radius of the path. Since the velocity in a circular path is always tangential at any given point and the acceleration is along the radius, we can say that they are perpendicular to each other, since it is a known fact that the radius of the circle at any point is perpendicular to the tangent at that point.
Hence the situation mentioned in the statement (b) is also possible.

Note
We could have explained the statement (b) using the concept of projectile motion as well. The path of projectile motion is in the form of an arc, but if we break the entire length of the path into small parts, each part can be said to the arc of a circle. Now the velocity of the particle at each point will be tangential to the path at that point, and the acceleration will act along the radius of the circle formed by the part of the path. We can again say that the acceleration is perpendicular to the velocity.
The approach given in note can be a bit tricky so you should stick with the solution for better understanding.