question_answer

A particle starts from rest at t = 0 and undergoes an acceleration a in m s~2 with time (in seconds which is shown in figure. Which one of the following plot represents velocity v in \[m{{s}^{-1}}\text{ }verus\]time t sec?

A)

B)

C)

D)

Correct Answer: A

Solution :

From \[a-t\]graph we observe that

For \[t=0\operatorname{s}\,to\,t=2\,\operatorname{s};\]a is positive i.e., a>0.

So, v-t graph will be a straight line with positive slope. For \[t=2s\] to \[t=4s,\] a is negative (a<0), so v-t graph will be a straight line with negative sope. Complete v-t graph will be;

We can also verify that, velocity at \[\operatorname{t}=2s\]

=Area under (a-t) graph for \[t=0\,\operatorname{to}\,t=2s\,\]

\[=3\times 2=6m/s\]

\[\therefore v=6m/s\]