a
MOTION
Short Answer Type Questions
17. Is the uniform circular motion accelerated ? Give reasons for
18. Write the formula to calculate the speed of a body moving along a circular path. Give the meaning of each
your answer
symbol which occurs in it.
19. Explain why, the motion of a body which is moving with constant speed in a circular path is said to be
accelerated.
20. What is the difference between uniform linear motion and uniform circular motion ? Explain with examples.
21. State an important characteristic of uniform circular motion. Name the force which brings about uniform
circular motion.
22. Find the initial velocity of a car which is stopped in 10 seconds by applying brakes. The retardation due to
brakes is 2.5 m/s2.
23. Describe the motion of a body which is accelerating at a constant rate of 10 m s2. If the body starts from rest,
how much distance will it cover in 2 s?
24. A motorcycle moving with a speed of 5 m/s is subjected to an acceleration of 0.2 m/s2. Calculate the speed of
the motorcycle after 10 seconds, and the distance travelled in this time.
25. A bus running at a speed of 18 km/h is stopped in 2.5 seconds by applying brakes. Calculate the retardation
produced.
26. A train starting from rest moves with a uniform acceleration of 0.2 m/s2 for 5 minutes. Calculate the speed
acquired and the distance travelled in this time.
Answers
Explanation:
17) Yes, uniform circular motion is accelerated because the velocity changes due to continuous change in the direction of motion.. Due to this it is considered as accelerated motion
18) In order to calculate the speed of the body along a circular path, one should divide the circumference of the circle by the time (t) taken to traverse the circle. Therefore the total circumference of the circle =2*pi*r.
19) The motion of a body which is moving with constant speed in a circular path is said to be accelerated because its velocity changes continuously due to the continuous change in the direction of motion.
20) In uniform linear motion, the speed and direction of motion is fixed and so, it is not accelerated. Example- A car running on a straight road. In uniform circular motion, the speed is constant but the direction of motion changes continuously and hence, it is accelerated. Example- Motion of earth around the sun.
21) An important characteristic of uniform circular motion is that the direction of motion in it changes continuously with time, so it is accelerated.
Centripetal force brings about uniform circular motion.
22) Initial velocity, u=?
Final velocity, v=0m/s (car is stopped)
Acceleration, a=−2.5m/s
2
(negative because it is retardation)
Time, t=10s
Use the relation of the first equation of motion:
v=u+at
0=u+(−2.5)×10
u=25m/s
23) As the body is moving in constant acceleration, the motion of the body is linear. If the body starts from rest means its initial velocity is zero which is represented mathematically as u = 0. The acceleration is constant i.e. and the time covered will be t = 2s.
24) Given that
The initial speed of car=u= 5 m/s
Acceleration =a=0.2m/s2
Time=t=10s
We need to calculate the distance
We know that
v = u + at
= 5 + 0.2×10
= 5+2
= 7 m/s
s = ut + 1/2at²
= (5×10) + (1/2)×(2/10)×(10×10)
= 50 + 10
= 60 m
Final speed = 7 m/s
Distance traveled in 10 seconds = 60 m
25) Initial velocity, u=18 km/h
u=18×
3600
1000
=
3600
18000
m/s=5m/s
Final velocity, v=0 m/s
Time, t=2.5 sec
Acceleration, a=?
Using, v=u+at
a=
t
v−u
=
2.5
0.5
=−2m/s
26) Initial velocity, u=0m/s
Final velocity, yv=?
Acceleration, a=0.2m/s
2
Time, t=5min=5×60=300sec
Using first equation of motion to obtain the final speed:
v=u+at
v=0+0.2×300=60m/s
And the distance travelled is
s=ut+
2
1
αt
2
s=0×300+
2
1
×0.2×300×300
s=0+9000=9000m=9km
17.
An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards.
18.
In order to calculate the speed of the body along a circular path, one should divide the circumference of the circle by the time (t) taken to traverse the circle. Therefore the total circumference of the circle =2*pi*r.
19.
The motion of a body which is moving with constant speed in a circular path is said to be accelerated because its velocity changes continuously due to the continuous change in the direction of motion.
20.
In uniform linear motion, the speed and direction of motion is fixed and so, it is not accelerated. ... In uniform circular motion, the speed is constant but the direction of motion changes continuously and hence, it is accelerated. Example- Motion of earth around the sun.
21.
An important characteristic of uniform circular motion is that the speed remains constant while the direction of motion changes continuously with time, so it is accelerated.
Centripetal force brings about uniform circular motion.
22.
Initial velocity,
a = dv/dt
2.5 = v/10
So, v = 2.5*10 = 25 m/s
23.
Distance covered,
s = 1/2 * a*t*t
= 0.5*10*2*2 = 20 m
24.
u = 5 m/s
a = 0.2 m/s^2
t = 10 sec
Then
Speed after 10 sec,
V = u + at
= 5 + 0.2*10
= 5+5 = 10 m/s
And distance covered
s = ut + 1/2*a*t*t
s = 5*10 + 0.5*0.2*10*10
= 50 + 10 = 60
25.
Speed = 18 km/h
= 18*1000/3600
= 18*10/36 = 5 m/s
Time = 2.5 sec
Retardation produced = s/t
= 5/2.5 = 2 m/s^2
26.
u = 0 m/s
a = 0.2 m/s^2
t = 5 min = 300 sec
Then
Speed after 300 sec,
V = u + at
= 0 + 0.2*300
= 0+60= 60 m/s
And distance covered
s = 1/2*a*t*t
s = 0.5*0.2*300*300
= 9000 m
= 9 km