The engine of a motorcycle can produces a maximum acceleration 5m/s2. Its brakes can produce a maximum retardation 10m/s2. What is the minimum time in which it can cover a distance of 1.5 km?
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Answer:
Given,
Acceleration=5m/s
2
Retardation=10m/s
2
Dirtance=1.5km=1500m
S
1
=
2
1
(5)t
1
2
s
2
=
2
1
(10)t
2
2
V=5t
1
5t
1
−10t
2
=0
t
1
=2t
2
Since s
1
+s
2
=1500m
Therefore,
2
1
(5)t
1
2
+
2
1
(10)t
2
2
=1500
=
2
1
(5×4t
2
2
+10t
2
2
)=1500
since t
1
=2t
2
=
2
1
30t
2
2
=1500
t
2
=10s
So, t
1
=20s
Thus the total time is t
1
+t
2
10+20=30s
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