Question

The velocity of an object is given as a function of time by v = 4t − 3t2

, where v is in m/s and t is in seconds. Its

average velocity over the interval from t = 0 to t = 2s:

(A) is 0 (B) is −2m/s (C) is 2m/s (D) is −4m/s​

Answer 1

ANSWER

GIVEN:

4t-3t²=v

4(2-0)-3(2-0)²=v

v=8-3(4)

v=8-12

v= -4m/s

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Answer 2

Answer:

The average velocity is over the given time interval is zero.

Explanation:

Given the velocity of an object, $v = 4t - 3t^{2}$

And the time interval, $t = 0~ to ~2s$

Velocity is defined as the rate of change of displacement, given by $v=\frac{ds}{dt}$

$\implies ds=vdt$

integrating on both sides, with limits of time,

$\int ds=\int\limits^2_0 (4t - 3t^{2})dt$

$\implies s=\Big|\frac{4t^{2} }{2} - \frac{3t^{3} }{3}\Big|\limits^2_0$

$=\frac{4\times 2^{2} }{2} - \frac{3\times 2^{3} }{3}$

$=8 - 8=0$

Average velocity is defined as the displacement over the total time taken.

Since, the displacement is zero, therefore the average velocity is also zero.

Therefore, the correct answer is option 1.