THE COPPERBELT UNIVERSITY
SCHOOL OF MATHEMATICS AND NATURAL SCIENCES
DEPARTMENT OF PHYSICS
2020/2021 PH 110-INTRODUCTORY PHYSICS LECTURE
NOTES
COMPILED BY MULENGA MUMA © 2021
1
COMPILED BY MULENGA MUMA © 2021
2
COMPILED BY MULENGA MUMA © 2021
3
COMPILED BY MULENGA MUMA © 2021
4
COMPILED BY MULENGA MUMA © 2021
5
COMPILED BY MULENGA MUMA © 2021
6
COMPILED BY MULENGA MUMA © 2021
7
COMPILED BY MULENGA MUMA © 2021
8
COMPILED BY MULENGA MUMA © 2021
9
COMPILED BY MULENGA MUMA © 2021
10
COMPILED BY MULENGA MUMA © 2021
11
COMPILED BY MULENGA MUMA © 2021
12
COMPILED BY MULENGA MUMA © 2021
13
COMPILED BY MULENGA MUMA © 2021
14
COMPILED BY MULENGA MUMA © 2021
15
COMPILED BY MULENGA MUMA © 2021
16
COMPILED BY MULENGA MUMA © 2021
17
EXERCISES
1. The fastest 100 m that was ever run was in 9.58 s by Usain Bolt. What was his average
velocity in
(a) m/s?
(b) km/min?
(c) km/h?
[(a)10.4 m/s (b)0.63 km/min (c) 37.6 km/h]
2. A car covers first half of the distance between two places at a speed of 40 km/h and the
second half at 60 km/h. What is the average speed of the car?
[48 km/h]
3. On a 60 km straight road, a bus travels the first 30 km with a uniform speed of 30 km/h.
How fast must the bus travel the next 30 km so as to have average speed of 40 km/h for
the entire trip?
[60 km/h]
4. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed
again 5 steps forward and 3 steps backward and so on. Each step is 1m and requires 1
second. Plot position-time graph for his motion. From the graph or otherwise find the time
taken by him to fall in a pit 13 m away from start. [Hint: In 8 seconds he moves forward
by 2 m; total time t=37s]
5. The position-time graph shown in figure 3.8 represents the motion of a basketball coach
during the last 8 seconds of the game in overtime.
(a)Find the average velocity in the time intervals
(i)
0 to 2 s,
(ii)
0 to 4s,
(iii)
2 s to 4 s,
(iv)
4 s to 7 s,
(v)
0 to 8 s.
[(i) 5 m/s (ii) 1.25 m/s (iii) -2.5 m/s (iv) -3.3 m/s (v) 0]
(b) Repeat part (a) for the average speed.
[5 m/s; 3.75 m/s; 2.5 m/s; 3.3 m/s; 3.75 m/s]
COMPILED BY MULENGA MUMA © 2021
18
Figure 3.8 See exercise 6
6. A lion starts at rest 26 m away from a clueless tourist and moves towards him at a constant
velocity of 50 km/h. It takes the tourist 1 second to react to the lion, turn around and begin
running at velocity of 5 m/s towards his vehicle. The vehicle is parked 6 m away from
him and on the same axis as the lion’s path. If the tourist escapes, how far behind him is
the lion? If the tourist is caught, how far is he from the vehicle? [The tourist escapes and
the lion is 1.4 m behind him]
7. A position-time graph for a particle moving along the x axis is shown in figure 3.9.
(a) Find the instantaneous velocity at time t = 2 seconds
(b) At what value of t is the velocity zero?
[(a) -3.8 m/s (b) 4s]
Figure 3.9 See exercise 7
COMPILED BY MULENGA MUMA © 2021
19
8. A particle starts from rest and accelerates as shown in the figure 3.10. Determine
(a) the particle’s speed at t = 10 s and at t = 20 s.
(b) the distance traveled in the first 20 seconds.
[(a) 20 m/s; 5 m/s (b) 262 m]
Figure 3.10 See exercise 9
9. A velocity–time graph for an object moving along the x direction is shown in the figure
3.11.
a) Plot a graph of the acceleration versus time.
b) Determine the average acceleration of the object in the time intervals
i. t = 5 s to t = 15 s
ii. t = 0 to t = 20 s.
[(b) (i)1.6 m/s2; (ii)0.8 m/s2]
Figure 3.11 See exercise 10
COMPILED BY MULENGA MUMA © 2021
20
10. The Lamborghini Murcielago can accelerate from 0 to 62.2 mi/h in a time of 3.4 seconds.
Determine the acceleration of this car.
[ 8.18 m/s2]
11. A car passes a point and then 120 m away, its velocity was 21 m/s. If its acceleration was
constant at 0.583 m/s2, what was the car’s velocity at that point?
[17.4 m/s]
2
12. A sprinter from rest accelerates at 1.5 m/s for the first 20 m but then gets tired and
decelerates at -0.1 m/s2 for the next 80 m. What is the sprinter’s final velocity? [6.64 m/s]
13. An out-of-control train is hurling down the track at 35 m/s. If the conductor sees a kitten
on the track 200 m in front of him, with what minimum acceleration would the train need
to save the adorable kitten?
[-3.06 m/s2]
14. Two trains, one travelling at 72 km/h and the other one at 144 km/h, are headed toward
one another along a straight level track. When they are 950 m apart, each engineer see’s
the other’s train and applies breaks. If the breaks decelerate each train at the rate of 1m/s2,
determine if there is a collision.
[yes]
15. A bullet strikes a uniform plank with a velocity of 400 m/s and comes out with half
velocity. What would be the velocity if the plank were only half thick?
[316.2m/s]
16. A person is running at his maximum speed of 4 m/s to catch a train. When he is 6m from
the door of the train, it starts moving at a constant acceleration of 1 m/s/s. How long does
he take to catch the train?
[2 s]
2
17. A particle moves along the x-axis according to the equation 𝑥 = 2 + 3𝑡 − 𝑡 , where 𝑥 is in
metres and 𝑡 is in seconds. At 𝑡 = 3 s, find
a) the position of the particle
b) the velocity of the particle
c) the acceleration of the particle.
[(a) 2 m (b) -3 m/s (c) -2 m/s2]
18. A particle moves along a straight line with an acceleration 𝑎 = 3𝑡2 − 2, where 𝑎 is in ms-2
and 𝑡 is in seconds. Initially, the particle is at O, with velocity 2 m/s. At 𝑡 = 3 s, find the
a) acceleration of the particle
b) velocity of the particle
c) position of the particle.
[(a)25 m/s2 (b)23 m/s (c)17.25 m]
19. Two parallel rail tracks run north-south. Train A moves north with a speed of 54 km/h
and train B moves south with a speed of 90 km/h. What is the relative velocity in m/s of.
(a) B with respect to A
(b) the ground with respect to B
(c) a monkey running on the roof of train A against its motion (with velocity 18 km/h with
respect to A) as observed by a man standing on the ground.
[-40m/s; 25m/s; 10m/s]
20. According to Guinness, the tallest man to have ever lived was Robert Pershing of Alton,
Illinois. He was last measured in 1940 to be 8.92 ft. Determine the speed which a quarter
would have reached before contact with the ground if dropped from the top of his head.
[7.3 m/s]
21. A stone thrown vertically up from the top of a tower with a velocity 20m/s reaches the
ground in 6 seconds. Find the height of the tower.
[56.4 m]
22. Particle A is thrown vertically upward from the bottom of a building 80 m high s. At the
same instant particle B is dropped from the top. The two particles collide after 2s. Find
the initial velocity of particle A. Assume they are moving along the same vertical line,
and that air resistance can be neglected (use g = 10 m/s2)
[40 m/s]
COMPILED BY MULENGA MUMA © 2021
21
23. A particle moves in the xy plane such that, at time t, its displacement from a fixed point
O is given by r = 4t𝒊 + (3t−5t2)j. Find the magnitude and direction of the velocity when
t=0. Show that the acceleration is constant. Do you notice anything significant about this
acceleration?
[v = 5 m/s; 𝜽 =370]
24. A bomb is released from an aircraft when it is at height 1960 m above a point A above
the ground and is moving horizontally at a speed of 100 m/s. Find the distance from A to
the point where the bomb strikes the ground.
[2 km]
25. A railcar is moving horizontally with speed of 24 m/s and decelerating at 3.65 m/s2 when
a light bulb 2.55 m above the floor comes loose and drops. Where, relative to the point
directly below its original position, will the bulb strike?
[0.98 m]
26. A hot-air balloon having 20 m/s constant velocity is rising vertically from the ground to
up. When the balloon reaches 160 m height, an object from the balloon is thrown
horizontally with a velocity of 40 m/s with respect to the balloon. Find the horizontal
distance travelled by the object. (use g = 10 m/s2)
[320 m]
27. A short is fired from a gun on the top of a hill 90 m high with velocity 80 m/s at an angle
300 with the horizontal. Find its horizontal distance from the point of projection when it
strikes the ground.
[𝟒𝟎𝟎√𝟑 m]
0
28. You throw a rock off the cliff at 10 m/s, 20 above the horizontal. The cliff is 25 m high.
With what angle does it the rock hit the ground?
[67.2 0]
29. A projectile is launched on level ground. At the peak of its trajectory, it is 7.5 m high. It
lands 10 m from where it was launched. At what angle was the projectile launched?[72 0]
30. Prove that for a projectile fired from the surface of a level ground at an angle 𝜃0 above
the ground, the ratio of the maximum height H to the range R is given by
𝐻 ⁄𝑅 =
COMPILED BY MULENGA MUMA © 2021
1
tan 𝜃0
4
22