# Problem and Solutions in One Dimensional Motion

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Question 1
A stone is thrown vertically upwards with a initial speed of 10 m/s from the edge of the roof of the house of Height H=20 m
a) how long does it takes for the stone to hit the ground
b) At what velocity it will hit the ground
Solution
t=3.28 sec
v=-22.2 m/s

Question 2
A body fell from rest from a height H above the ground. In the last 1 sec of the its fall, it travelled a distance H/2 . Find the value of H
Solution
H=57.1 m

Question 3
If the body loses half of its velocity on penetrating 3 cm in the wooden block,then how much will it penetrate more before coming to rest?
Solution
1 cm

Question 4
A car brakes from a speed of 108 km/h to 72 km/h duing a displacement of 100m. What is its acceleration?
Solution This can be easily found using Third Kinematics equations
v2=u2+2as
a=-2.5 m/s2

Question 5
A Ball is dropped from a building of the height 90 m . Simultanously another ball is thrown up with a speed of 40 m/s. Calculate the Relative speed of the balls as a function of time?
Solution
Both the balls are falling freely under gravity .Therefore no acceleration of one with respect to other .So relative speed of the balls remains constant equal to 40m/s

Question 6
The Relation between t and distance x is given by
t=ax2 +bx where a and b are constant.
Expreess instaneous acceleration in terms of instaneous velocity
Solution
acceleration =-2av3

Question 7
A car travels 100 km in 2 hours and 50 km in 1 hour in the same direction.
a) What is the Car's average speed for the whole journey?
b) What is the Car's average velocity for the whole journey?
Solution
50km/h,50km/h

Question 8
Two balls of different masses (one lighter and other heavier) are thrown vertically upwards; with the same speed. Which one will pass through the point of projection in their downward direction with the greater speed?
Solution
In case of motion under gravity, the speed with which a body returns back is always equal to the speed with which it is thrown up. Since expression for final speed does not involve mass, both the balls will acquire the same speed.
Question 9
A Stone is thrown Up, what is the velocity, acceleration at the top and what direction?
Solution
At the peak,velocity of the stone is zero but accleration is not zero, acceleration is equal to acceleration due to gravity and it is acting downwards

Question 10
What does the slope of the velocity-time graph shows?
Solution
Acceleration

Question 11
What does the area under the velocity time graph represent
Solution
Displacement

Question 12
Give example of the motion where x>0, v < 0 and a > 0?
Solution
x= p +qe-t Where p and q > 0
So x > 0 at any instant
Velocity(dx/dt) = d(p +qe-t)/dt= -qe-t ( v < 0)
Acceleration(dv/dt) = d(-qe-t)/dt= qe-t ( a > 0)

Question 13
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 14
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 15
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 16

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