Question

Velocity time equation of a particle moving in a straight line is V = t2 - 5t + 6. The distance travelled by the particle in the time interval from t = 0 to t = 4
sec
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Answer 1

Answer:

20:4wg velocity time

Explanation:

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Answer 2

The distance traveled is 5.33 m

The velocity time equation of the particle moving in a straight line is,

v = t² - 5t + 6

We know,

Velocity, v = ds/dt, Where s = Distance traveled by the particle

                                           t = time taken

∴ ds/dt = t² - 5t + 6

⇒ ds = (t² - 5t + 6) dt

∴ ∫ds = ∫(t² - 5t + 6) dt

⇒ s = $\frac{t^{3} }{3} - \frac{5}{2} t^2 + 6t$

As the time interval of the particle is 0 to 4 sec, the limits of the integration would be 0 and 4.

∴ s = 64/3 - 40 + 24

⇒ s = 5.33

So, the  distance traveled by the particle in the time interval from t = 0 to t = 4 sec is 5.33 m.