Question

If the particle is moving along a straight line given by relation x=2-3t+4t^3 where s is in cms.,and t in sec.its average velocity during the 3rd sec.

Final ans. Is 73 cm/s. Please explain with steps.

Answer 1

So basically first u select the time interval which in our case is from t=2sec to t=3sec.
Further see the attachment
Hope it helps.....
:)

Answer 2

Answer:

73 cm/sec

Explanation:

Given:

The particle follows the relation's straight line of motion.

$x=2-3t+4t^{3}$

To find:

Average velocity in 3rd sec

Solution:

The definition of average velocity states that it is the product of an object's displacement from point a to point b and the time it takes to complete that displacement. It should be noticed that we emphasise direction by emphasising movement rather than distance.

We know that,

average velocity = $\frac{totaldisplacement}{total \\time \\taken}$

Here, $x=2-3t+4t^{3}$

Total displacement in the third second can be calculated by,

S(3)-S(2)

Thus, S(2) =

$=2-3(2)+4(2^{3} )\\=2-6+32=28$

Similarly S(3)=

$=2-3(3)+4(3^{3} )\\=2-9+108=101$

So, S(3)-S(2) = 101-28=73cm

Now, finding the average velocity,

$V_(avg)=\frac{73}{1}=73cm/s$

Hence the correct answer is 73 cm/s.

What mean by average velocity.

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