Question

for a particle traveling along x axis position depends on time according to the equation x=3t^2 where x is in cm and t is in sec then what is the average velocity from t=1sec to t=2sec​

Answer 1

Given:

Particle travelling along x axis depends on time as follows ;

x = 3t².

To find:

Average velocity from time 1 - 2 sec.

Concept:

Average velocity is the ratio of Total Displacement to the Total Time taken to cover that distance.

Calculation:

Displacement in the specified time-interval :

$\therefore \: x = 3 \bigg \{ {t}^{2} \bigg \}_{1}^{2}$

$= > x = 3 \bigg \{4 - 1 \bigg \}$

$= > x = 9 \: cm$

So , average velocity will be :

$\therefore \: avg. \: v = \dfrac{total \: \: displacement}{total \: \: time}$

$= > \: avg. \: v = \dfrac{9}{2 - 1}$

$= > \: avg. \: v = \dfrac{9}{1}$

$= > \: avg. \: v = 9 \: cm {s}^{ - 1}$

So , final answer is :

Average velocity of the object is 9 cm/s.