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A particle moves along a line so that its velocity at time t is v(t)= t^2-t-6 m/s
a) Find the displacement of the particle during the time period 2< or equal to t< or equal to 4
and interpret the result.
b) Find the distance traveled during this time period.

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The expert finds the distance traveled during this time period.

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A particle moves along a line so that its velocity at time t is v(t)= t2-t-6 m/s.

a) Find the displacement of the particle during the time period 2 < t < 4
and interpret the result.

b) Find the distance travelled during this time period.

Solution: Velocity v(t) = dx/dt = t2 - t - 6 ....... (1) where x represents the displacement of the particle.

dx = (t2 - t - 6)dt

Integrating we get: ∫dx = ∫(t2 - t - 6)dt

Displacement x = t3/3 - t2/2 - 6t + C ...........(2) where C is the constant of integration

Assuming at t = 0, x = 0. Substituting in (2) we get C = 0. ...

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