1D Kinematics Problems And Solution

Question 1. A ball is dropped vertically from a height h above the ground .It hits the ground and bounces up vertically to a height h/2.Neglecting subsequent motion and air resistance ,its velocity v varies with the height h as









Solution(1):
. Before hitting the ground ,the velocity v is given by v²=2gd Which is a quadratic equation and hence parabolic path. Downward direction means negative velocity , After collison ,the velocity becomes positive and velocity decreases Further v₁²=2g(d/2)=gd Therefore v=v₁√2 As the direction is reversed and speed is decreased, Hence (a) is the answer 

Question 2. The displacement -time graph of a moving particle is shown below.The instantaneous velocity of the particle is negative at the point



a. C
b. D
c. E
d. B

Solution(2):
. The instantaneous velocity is given by the slope of the displacement time graph.
Since slope is negative at point B, instantaneous velocity is negative at B
Hence (d) is correct 

Question 3.The velocity -time graph of a moving particle is shown below.Total displacement of the particle during the time interval when there is nonzero acceleration and retardation is 



a. 60m
b. 40m
c. 50m
d. 30m

Solution(3):
. Acceleration is given by the slope of the velocity time graph
Non zero acceleration happened in the time interval 20 to 40 sec as the slope of the graph is non zero in that time interval

Now displacement in that interval is given by the area enclosed the v-t curve during that interval

So area=(1/2)20*3 +20*1=50m
Hence (c) is correct 
Question 4. Figure below shows the displacement -time graph of two particles.Mark the correct statement about their relative velocity


a. It first increases and then decreases
b. It is a non zero constant
c. it is zero
d. none of the above
Solution(4):
. The instantaneous velocity is given by the slope of the displacement time graph.
As slope of both the particle displacement time graph is constant.That means there individual velocities are constant.
So relative velocity is also constants
so it is a non zero constant as they have different velocity
Hence (b) is correct 

More Practice Problems
Question 1
A Jeep starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110m. Determine the acceleration of the Jeep.
Question 2
John is riding the Giant Drop at Canada. If John free falls for 2.6 seconds, what will be his final velocity and how far will he fall?
Question 3
A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.
Question 4
A feather is dropped on the planet other than earth which has very low acceleration due to gravity from a height of 1.40 meters. The acceleration of gravity on the other planet is 1.67 m/s2. Determine the time of feather to fall to the surface of the other planet
Question 5
The motion of a particle is described by the equation u=at.The distance travelled by the particle in first 4 sec is?
Solution
8a
Question 6
Three different objects of masses 5kg,6kg and 7 kg are allowed to fall from the same point O along three different frictionless path.What is the ratio of the speeds of the objects on reaching the grounds
Solution
1:1:1
Question 7
A truck moves from point A to B with a uniform speed a and returns from B to A with the uniform speed of b. What is the average speed of the round trip
Solution
2ab/(a+b)