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Math Help - Mechanics, two questions

  1. #1
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    Mechanics, two questions

    Q1-A truck with initial velocity 6 m/s^-1 brakes and comes to rest. At time t seconds after the brakes are applied with acceleration a m/s^-2 where a=-3t. This formula applies until the truck halts.

    1: Find time taken for the truck to halt.
    2:Find distance traveled whilst decelerating.
    3:Find greatest deceleration of truck?

    Q2-A force of (36-t^2) newtons acts at time t seconds on a particle of mass 1kg. When t=0 the particle has velocity 2m/s^-1 in the direction of the force. Find the velocity of the particle when t=6 and find the distance travelled between t=0 and t=6.

    Could somebody please help me out, been stuck for ages Many thanks in advance.
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  2. #2
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    a = -3t

     <br />
v(t) = \int -3t \, dt = -\frac{3t^2}{2} + C<br />

    v(0) = 6 \, m/s ... 6 = 0 + C

     <br />
v(t) = -\frac{3t^2}{2} + 6<br />

    1) set v(t) = 0 and solve for t

    2) d = \int_0^{t_1} v(t) dt , where t_1 is the time found in question (1).

    3) think about it ... when will -3t have its greatest magnitude?
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  3. #3
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    Quote Originally Posted by skeeter View Post
    a = -3t

     <br />
v(t) = \int -3t \, dt = -\frac{3t^2}{2} + C<br />

    v(0) = 6 \, m/s ... 6 = 0 + C

     <br />
v(t) = -\frac{3t^2}{2} + 6<br />

    1) set v(t) = 0 and solve for t

    2) d = \int_0^{t_1} v(t) dt , where t_1 is the time found in question (1).

    3) think about it ... when will -3t have its greatest magnitude?
    Thanks for your help. I have done parts one and two and got t=2 and 8m for distance travelled, in relation to magnitude, I am still stuck .

    Can anybody help me out with Question 2? Im so puzzled
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  4. #4
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     <br />
a(t) = -3t<br />

     <br />
a(0) = 0<br />
     <br />
a(1) = -3<br />
     <br />
a(2) = -6<br />

    what is the greatest magnitude for a ?

    btw, magnitude of a would be |a|
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