The velocity of an object moving in a straight line path is given as a function of time by v = 6t–3t², where v is in m/s, t is ins. The average velocity of the object between t=0 and t=2 seconds is

Given, velocity, v = 6t − 3t²

As we know that,

v = dx/dt​

Here, x is the displacement of the particle.

Now, dx = vdt

Integrate on both sides, limit t=0 to t=2, and we get

∴ x = ₀∫²​vdt = ₀∫²​(6t − 3t²)dt

= [6t²/2​]₀²​ − [3t³/3​]₀² ​= [3t2]₀^2​ − [t3]₀²​

= [3(2)² − 3(0)²] − [(2)³ − (0)²]

= [12 − 0] − [8 − 0] = 12 − 8 = 4m

Average velocity, v_avg ​=  ( Total displacement)/(Total time taken) ​ = 4/2 ​=2m/s

Hence, the average velocity of the object between

t=0 to t=2s is 2m/s