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Question

The acceleration of a cart started at t =0, varies with time as shown in figure (3-E2). Find the distance travelled in 30 seconds draw the position-tome graph.

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Solution

In fiirst 10 sec,S1=ut+12 at2
=0+12 5.102=250ft
v=u=at
=0+5×10=50ftsec

From 10 to 20 sec Δ=20-10=10 sec) it moves with uniform velocity of 50 ftsec)
Distance, S2=50×10=500ft
Between 20 sec to 30 acceleration is constant i,e.-5fts^2

At 20 sec, velocity is 50ftsec
t=30-20=10 s

S3=ut+12at2
50×10+12(5)102
=500-250=250 m

Total distance travelled is 30 sec

=S1+S2+S3
=250+500+250
=1000 ft



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