Question

In the given graph, find the velocity of particle at t=6 s. (Initial velocity = 5 m/s)
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Answer 1

Explanation:

7m/s

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Answer 2

The velocity of the particle after 6 seconds is 7 m/s

Explanation:

The given graph is acceleration vs time

We know that rate of change of velocity is acceleration

i.e. $\frac{dv}{dt}=a$

or, $\int dv=\int adt$

i.e. the area under the acceleration-time graph will give us velocity

Since the initial velocity is 5 m/s

∴ At t= 6 seconds, the velocity of the particle will be

= 5 + Area of the triangle above the time axis - Area of the triangle below the time axis

$=5+\frac{1}{2}\times 2\times 4-\frac{1}{2}\times (6-4)\times 2$

$=5+4-2$

$=7$ m/s

Thus, the velocity of the particle after 6 seconds is 7 m/s

Hope this answer is helpful.

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