The velocity function of a particle moving along a line is given by the equation v(t)...

The velocity function of a particle moving along a line is given by the equation v(t) = t² - 2t -3. The particle has initial position s(0) = 4.

a. Find the displacement function

b. Find the displacement traveled between t = 2 and t = 4

c. Find when the particle is moving forwards and when it moves backwards

d. Find the total distance traveled between t = 2 and t = 4

e. Find the acceleration function, and use it to find the acceleration of the particle at t = 3

Solutions

Expert Solution

The displacement function is given by

, by Applying the initial condition s(0)=4, we will get s(t).

The displacement travelled between the time t=2 and t=4 is given by, s=s(4)-s(2) and the distance travelled between t=2 and t=4 is given by d=||s(4)|-|s(2)||. The particle moves forward if the velocity is positive and backward when velocity is negative.

The acceleration function is defined as the rate of change in velocity, i.e, a(t)=v'(t).

milcah answered 1 year ago

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