Mr. Rohit was driving a car of mass 1000 kg with a constant speed of 72 km/h to go to his office. Suddenly he realized that he will be late for office and increased the speed of the car to 90 km/h in 10 seconds.
(i) The change in momentum of the car is
(a) zero (b) 18000 kg m/s (c) 90000 kg m/s (d) 5000 kg m/s
(ii) The force produced by the automobile engine of the car is(a) zero (b) 1800 N (c) 9000 N (d) 500 N
(iii) The acceleration produced by the automobile engine of the car is
(a) 0.5 m/s2 (b) 18 m/s2 (c) 1.8 m/s2 (d) 5 m/s2
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Answer:
Solution
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Net acceleration is due to braking and centripetal acceleration
Due to Braking,
a
T
=0.5m/s
2
Speed of the cyclist, v=27km/h=7.5m/s
Radius of the circular turn, r=80m
Centripetal acceleration is given as:
a
c
=
r
V
2
=(7.5
2
)/80=0.70m/s
2
Since the angle between a
c
and a
T
is 900, the resultant acceleration a is given by:
a=(a
c
2
+a
T
2
)
1/2
a=(0.7
2
+0.5
2
)
1/2
=0.86m/s
2
tanθ=
a
T
a
c
where θ is the angle of the resultant with the direction of the velocity.
tanθ=
0.5
0.7
=1.4
θ=tan
−1
(1.4)=54.56
0
Explanation:
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