answer the following questions
1. if the velocity of a body is variable can the average acceleration be constant. if yes then give an example
2. which one of the following graph for a body moving along a straight line is possible.
explain with an example
Answers
Answer: 1) Yes.
2) Option 2 is correct
Explanation:
1) Yes. If the velocity of a body is variable then the average acceleration can be constant.
Suppose that if a particle is moving with the speed of v₁ , v₂ , v₃ , v₄ , v₅ ............ vₙ with the respective time,
t₁ , t₂ , t₃ , t₄ ..............tₙ
t = t₁ + t₂ + t₃ + t₄ + .................+ tₙ
We know that,
Average Acceleration = (Final Velocity - Initial Velocity)/Total Time Taken.
= (vₙ - v₁)/t
In the case of every same v₁ , vₙ and t, We shall get same acceleration. It doesn't depends on the v₂ . v₃ ..............vₙ₋₁ , when total time taken is same. Doesn't matter what are the values of time periods but total time should be same.
A good example of this case is Uniform Circular motion. We we take in a point P at any path of circular path. At point P, we shall have same time velocity after every round. Hence the difference (vₙ - v₁) will always be zero. Thus we have same acceleration every time at point P.
2) Option 3 is correct.
i) In the first as we see, we have two different speed at same time which is not possible for any kind of motion.
ii) In this case speed is going to be negative, which is not possible.
iii) It holds all the favourable conditions for motion of a particle in straight line.
iv) In this case we have two different position with increasing rate of time. This is possible for circular motion as we know that particle comes to same position after a time period.
Hence, Option 3) is correct