(Q) Choose the correct option(s) regarding acceleration of the particle :
(A) acceleration of particle at t=1.5 sec is 4 m/s^-2.
(B)acceleration of particle at t=3.5 sec is -4 m/s^-2.
(C) acceleration of particle from t=1 sec to t=3 sec is constant but non-zero.
(D) acceleration of particle from t=1 sec to t=3 sec is constant.
The velocity time graph of a particle moving along a straight line is shown in the figure. In the time interval from t = 0 to t = 8 second, answer the following three questions.
Graphic
Dear Student,
We know that, slope of V-T graph gives the acceleration.
So,
Case 1, acceleration of particle at t=1.5 sec
It is evident from the graph that at 1.5 s, the graph has straight line. Thus, there is no change in the velocity.
The inst. acceleration will be 0 m/s2. Thereofore, it is wrong statement.
Case 2, acceleration of particle from t=1 sec to t=3 sec is constant but non-zero.
This statement is false, as when there is no change in velocity then the acceleration would be 0 (as it is both a constant and zero).
Case 3, acceleration of particle at t=3.5 sec is -4 m/s^-2.
If see logically, the instantenous acceleration at 3.5 s will be a negative value but, we can not actually compute the value being graph is not upto scale. Also, numerical value 4 is not so accurate (say for example if the change in velocity is - 0.5 m/s and t = 3.5 s the a = - 0.14 m/s2) Thus, this statement is also false.
Case4, acceleration of particle from t=1 sec to t=3 sec is constant.
This statement is true. As in this the acceleration is 0 m/s2, which is constant number.
Therefore, option 'D' is correct.
Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
We know that, slope of V-T graph gives the acceleration.
So,
Case 1, acceleration of particle at t=1.5 sec
It is evident from the graph that at 1.5 s, the graph has straight line. Thus, there is no change in the velocity.
The inst. acceleration will be 0 m/s2. Thereofore, it is wrong statement.
Case 2, acceleration of particle from t=1 sec to t=3 sec is constant but non-zero.
This statement is false, as when there is no change in velocity then the acceleration would be 0 (as it is both a constant and zero).
Case 3, acceleration of particle at t=3.5 sec is -4 m/s^-2.
If see logically, the instantenous acceleration at 3.5 s will be a negative value but, we can not actually compute the value being graph is not upto scale. Also, numerical value 4 is not so accurate (say for example if the change in velocity is - 0.5 m/s and t = 3.5 s the a = - 0.14 m/s2) Thus, this statement is also false.
Case4, acceleration of particle from t=1 sec to t=3 sec is constant.
This statement is true. As in this the acceleration is 0 m/s2, which is constant number.
Therefore, option 'D' is correct.
Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards