a train starts from rest from A station and travels with uniform acceleration of 0.5 metre per second square for 20 seconds it travels with uniform velocity for another 30 second the brakes are then applied so that a uniform retardation is obtained and the train comes to rest in for the 10 seconds sketch the velocity time graph of this motion using your graph calculate the total distance traveled by the trainhow can I calculate the total distance
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Total distance covered(s) = Distance during acceleration(s
1
) + distance during uniform motion(s
2
) + distance during retardation(s
3
)
For acceleration,
v=u+a∗t
v
max
=2×10=20 m/s
s=ut+(1/2)at
2
s
1
=(1/2)×2×10
2
=100 m
For uniform motion,
s=vt
s
2
=20×200
=4000 m
During retardation,
v=u+at
0=20+50t
=−0.4 m/s
2
s
3
=ut+(1/2)at
2
=20×50+(1/2)×(−0.4)×50
2
=500 m
Total distance travelled, s=s1+s2+s3=100+4000+500=4600 m
Total time taken, t=t
1
+t
2
+t
3
=260 s
Average velocity, v
avg
=
Total Time
Total Distance
=4600/260=17.69 m/s
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