Question

 

The distance x covered by a body moving in a straight line in time t is given by   

            

The acceleration of the body will vary as

Solution

Correct option is

None of these

 

  

        

Differentiating again, we have 

        

     

 is the acceleration. Using (i) in (ii) we have  

         

Buy it is given that x2 = t2 + 2t + 3.

Using this in eq. (iii) we get a = 2/x3.

SIMILAR QUESTIONS

Q1

 

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? 

 

Q2

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

Q3

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? 

Q4

 

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    

 

Q5

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

Q6

 

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

Q7

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?

Q8

 

A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped during the same time? 

 

Q9

A ball is thrown vertically downward with a velocity u from the top of a tower. It strikes the ground with a velocity 3u. The time taken by the ball to reach the ground is given by

Q10

Ball is called in a straight line with a speed of 5 ms–1 towards a bigger ballB lying 20 m away. After collision with ball B, full A retraces the path and reaches its starting point with a speed of 4 ms–1. What is the average velocity of ball A during the time interval 0 to 6 s?