Question

13. Prove that the uniform circular motion is an accelerated motion.
F. Solve the following numerical problems.
1. Ramesh goes from his residence to a market 2.5 km away. Finding the market closed, he returns back to his
residence. What is the distance covered by Ramesh? What is his displacement?
2. Samir travels on a straight road. He goes from position A to position B where the distance AB = 5 km. Now, he
turns back and travels a distance of 2 km to reach the position C. Find (a) the total distance travelled by Samir
during the entire journey, and (b) the magnitude of his displacement.
3. Kamini hired a taxi and noted the initial reading of its odometer as 24803 km. After the journey, she noted the
final reading of odometer as 25118 km. If the journey time was 4 hours 40 minutes, calculate the average speed
of the taxi during the entire journey.
4. At a certain instant, an auto driver is driving at a speed of 30 km h1 Then, he uniformly accelerates the auto
and after 2.5 minutes, the speed of his auto becomes 60 km h . What is the average speed of the auto? What is
the value of uniform acceleration during the given interval of time?
If the speed of laser signal be
3.0 x 108 ms), calculate the distance of the moon from the earth.
6. A bus starts from rest and attains a speed of 36 km h-1 in 1 minute while moving with uniform acceleration along
a straight road. Calculate the acceleration of the bus.
7. An athlete starts running from rest. He accelerates uniformly and completes 100 m race in 10 seconds. Find his
acceleration.
8. A metro train starts from a station and under uniform acceleration, it acquires a velocity of 72 km hin 10 s.
Calculate its acceleration and the distance covered during this time.
9. A car is running at a rate of 54 km h-. Suddenly, the driver applies brakes and stops the car within a distance
of 7.5 m. What is the acceleration produced by the brakes? Assume that the acceleration is uniform one.
5. Laser signal sent from the earth takes a time of 1.28 seconds to reach the man​

Answer 1

Step-by-step explanation:

uniform circular motion is an accelerative motion because in circular motion the velocity of the particle changes at every instance and change in velocity will respect of time is called acceleration hence circular motion is are accelerated motion

Now, Derivation of centripetal acceleration

Force of a moving object can be written

F=m×a....(1)

From diagram given above

PQ

+

QS

=

PS

−

V

1

+

V

2

=△V

△V=

V

2

−

V

2

The triangle PQS and AOB are similar hence

AB

△V

=

r

V

AB=arc,AB=V△t

V△t

△V

=

r

V

△t

△V

=

r

V

2

∴a=

r

V

2

centripetal acceleration

△t

△V

=

r

V

2

⇒a=

r

V

2

solution