Question

A stone is dropped from a height of 125 m. If g = 10 ms–2, what is the ratio of the distances traveled by it during the first and the last second of its motion? 

Solution

Correct option is

1 : 9

 

Since the initial velocity of the stone is zero, the total time taken by the stone to hit the ground is given by 

           

  

            

             = 5 s

During the first second, the stone falls a distance h1 given by

       

            

During the first four seconds, the stone falls a distance h given by

           

           

 Distance h2 through which the stone falls in the last (i.e. fifth) second

      = 125 – 80  

      = 45 m. 

.

SIMILAR QUESTIONS

Q1

 

The displacement y (in metres) of a body varies with time t (in seconds) as  

               

How long does the body take to come to rest?

Q2

A body goes from A to B with a velocity of 40 kmh–1 and returns from Bto A with a velocity of 60 kmh–1. What is the average velocity of the body during the whole journey?

Q3

The area under the velocity-time graph between any two instants t = t1and t = t2 gives the distance covered in time 

Q4

A particle is given a displacement of 4 m in the x-y plane. If the x-component of the displacement vector is 2 m, the y-component will be

Q5

 

A car, starting from rest, accelerates at a constant rate of 5 ms–2 for some time. It then retards at a constant rate of 10 ms–2 and finally comes to rest. If the total taken is 6 s, What is the maximum speed attained by the car? 

 

Q6

A body, starting from rest, moves in a straight line with a constant acceleration a for a time interval t during which it travels a distance s1. If continues to move with the same acceleration for the next time interval tduring which it travels a distance s2. The relation between s1 and s2 is

Q7

 

A body, moving in a straight line, with an initial velocity u and a constant acceleration a, covers a distance of 40 m in the 4th second and a distance of 60 m in the 6th second. The values of u and a respectively are    

 

Q8

A simple pendulum is hanging from the ceiling of a compartment of a train. It is observed that the string is inclined towards the rear of the train. If follows that the train is

Q9

 

The displacement of a body from a reference point, is given by

          

where x is in metres and t in seconds. This shown that the body is

Q10

A car moving at a speed v is stopped in a certain distance when the brakes produce a deceleration a. If the speed of the car was nv, what must be the deceleration of the car to stop it in the same distance and in the same time?