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The cart started at t=0,its acceleration varies with time as shown in figure. Find the distance travelled in 30 seconds and draw the position time graph.

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2 years ago

```							In t=0 to 10 s,acceleration f=10 m/s2.Initial velocity u=0 at t=0.Final velocity v at t=10s can be calculated fromv=u+ftOr,v=10×10=100 m/sDistance s travelled in this time can be calculated fromv2=u2+2fsor,s1=v2/2f=1000/2=500mIn the time interval t=10 to 20s,f=0.So particle moves with constant speed v=100m/s.So distance travelled is s2= vt=100×10=1000mIn the time interval t=20 to 30 second,f=-10m/s2.Initial velocity is u=100m/s and final velocityv=u+ftOr,v=100-100=0m/sDistance travelledv2=u2+2fs3Or,s3=500 m.So total distance travelled is 2000.To draw the graph for the 1st segment,f=10Or,d2x/dt2=10Integratingdx/dt=10t+cVelocity is zero at t=0.so c=0.Again integratingx=10t2/2=5t2It is a parabolaFor the second segment,f=0d2x/dt2=0Or,dx/dt=constant=say cIntegratingx=ct+c1This is a straight line.For the 3rd segmentx=-5t2+c2t+c3It is also a parabola.Please try to draw these in sequentially in a graph as I have no option of attaching file from my device.Hope this helps.
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2 years ago
```							In both cases draw half the parabola.Beacuse t is only positive here.In the 1st case the parabola is of the formy=x2.Draw only the right side of it starting from  origin.In the 3rd segment it is of the form y=-x2.In this case also draw only the right half of the parabola.
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2 years ago
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