1. Car travelled up a hill at constant speed of 10 𝑚𝑚𝑠𝑠 −1 and then returned down the hill at 20 𝑚𝑚𝑠𝑠 −1 . If the time to
turned around is ignored, a) what was the average speed round the trip? b) what was the average velocity round
the trip? [13.3 𝑚𝑚𝑠𝑠 −1 , 0 𝑚𝑚𝑠𝑠 −1]
2. A loaded truck is going at a speed of 36 𝑘𝑘𝑘𝑘ℎ−1 and a car starts at a point 3 km behind the truck with an
acceleration of 2 𝑚𝑚𝑠𝑠 −2 . When will the car overtake the truck? What is the distance covered by the car before it
overtakes the truck. [60 s, 3600 m]
3. A ball is projected vertically upwards with a velocity of 29.4 𝑚𝑚𝑠𝑠 −1 from the top of a tower so that it finds its path
below the top. Calculate a) the vertical displacement of the ball in 4.0 s b) the time taken by the ball to reach
maximum height c) the total distance it travels in 4.0 s d) the distance it travels in 8th second of its motion. [39.1
m up, 3 s,49.0 m, 44.1m]
4. When a ball is dropped from a height of 20 m, it rebounds with a velocity which is ¾ of the velocity with which it
hit the ground. Determine the time interval between the first and second bounces. [3 s]
5. A sand bag is released from a hot air balloon which is ascending with a steady vertical velocity of 8 𝑚𝑚𝑠𝑠 −1 . If the
sand bag hits the ground 15 s later, what was the height of the balloon above the ground when it was released.
[1005 m]
6. A stone is dropped from the top of a tower 60 m high. At the same time another stone is projected vertically
upwards from the ground with a velocity 20 𝑚𝑚𝑠𝑠 −1 . Find when and where will they meet? [45 m from top]
7. A body falls freely from the top of a tower and during the last second of its fall, it falls through 25 m. Find the
height of the tower. [45 m]
8. A stone is dropped from the top of a tall building and 1 sec later a second stone is thrown vertically down with a
velocity of 20 𝑚𝑚𝑠𝑠 −1 . When and where will the second stone overtake the first? [1.5 s, 11.25 m]
9. A person standing at the edge of a cliff throws a stone straight up with an initial velocity 20 𝑚𝑚𝑠𝑠 −1 . If the edge of
the cliff is 20 m from the ground below, with what velocity will the stone strike the ground? With what velocity
will the stone strike the ground. If the person throws it straight down with the same initial velocity. [28.3 𝑚𝑚𝑠𝑠 −1 ]
10. An object is dropped from the top of a tower of height 156.8 m and at the same time another object is thrown
vertically upward with the velocity of 78.4 𝑚𝑚𝑠𝑠 −1 from the foot of the tower, when and where the two objects
meet? [2s, 20 m from top]
11. A stone is thrown vertically upwards. The variation with time of the displacement s of the stone is shown in fig.
Assume air resistance is negligible and therefore the stone has constant acceleration g.
Calculate
i) the initial speed with which it was thrown upward. [12.3 ms-1]
ii) the speed at 3.0 s [17.2 ms-1]
iii) the distance travelled from t=0 to t=3.0 s [22.7 m]
iv) the displacement from t=0 to t=3.0 s. [7.4 m]
v) draw the variation with time t of the velocity v of the stone from t=0 to t=3.0 s.
12. What is the velocity of the object at t = 2 s. [1.8 ms-1]
13. An object was thrown up in an arbitrary planet. Velocity time graph of the object is given below.
Calculate
a) the velocity of the object in time t = 3 s. [3.4 ms-1]
b) acceleration of the object at time t = 2 s. [3.4 ms-2]
c) the displacement of the particle in t = 1 s [-5.1 m]
d) the displacement in time t = 3 s. [-5.1 m]
14. The variation with time t of the velocity of two cars P and Q is shown in fig.
The cars travel in the same direction along a straight road. Car P passes car Q at time t=0.
a) the speed limit for cars on the road is 100 kmh-1. State and explain whether car Q exceeds the speed limit.
b) Calculate the acceleration of car P. [0.33 ms-2]
c) Determine the distance between the two cars at time t=12 s. [84 m]
d) from time t=12 s, the velocity of each car remains constant at its value at t=12 s. Determine the time t at
which car Q passes car P. [26 s]