## Integration Kinematics IB math HL

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Integration Kinematics IB math HL

Kinematics, Integration, Integrals - IB Mathematics HL

How can we find the times at which a particle comes to rest when is moving in a straight line with acceleration $4t-22 m/sec^2$ and with initial speed $60 m/sec$?

Thanks
Jack

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Joined: Mon Jan 28, 2013 8:08 pm

### Re: Integration Kinematics IB math HL

Integration Kinematics IB math HL

We know that the acceleration $a=\frac{dv}{dt}$

So, $\frac{dv}{dt}= 4t-22\Rightarrow$

$\int \ dv=\int (4t-22) \ dt \Rightarrow v=2t^2-22t+c$

Next, we find the constant $c$ by setting the initial conditions of the problem (for t=0 , v=60)

$v(0)=2(0)^2-22(0)+c \Rightarrow 60=c$.

Therefore, the velocity function is

$v(t)=2t^2-22t+60=2(t-5)(t-6)$

The particle comes to rest when $v(t)=0\Rightarrow 2(t-5)(t-6)=0\Rightarrow$

$t=5 \ or \ t=6$

Hope these help!!
elizabeth

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Joined: Mon Jan 28, 2013 8:09 pm

### Re: Integration Kinematics IB math HL

Thank you Elisabeth!!
Jack

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm