Question

 

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? 

 

Solution

Correct option is

20 ms–1

 

Let t1 be the time during which the car has an acceleration a1 = 5 ms–2and t2 be the time during which the car has a deceleration a2 = –10 ms–2. Since the car starts from rest, the maximum speed attained by the car . For time interval, this v is the initial speed and the final speed is zero. Therefore,   

          

Thus,  

         

  

                 

                  = 2  

.   

Now,  

          

Therefore 

          t1 = 4 s and t1 = 2 s.   

Also  

         

            

             = 20 ms–1.

SIMILAR QUESTIONS

Q1

 

Two balls of masses m1 and m2 are thrown vertically upward with the speed u. If air resistance is neglected, they will pass through their point of projection in the downward direction with a speed 

 

Q2

A train covers half of its journey with a speed of 20 ms–1 and the other half with a speed of 30 ms–1. The average speed of the train during the whole journey is

Q3

 

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?

Q4

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?

Q5

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

Q6

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

Q7

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

Q8

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? 

Q9

 

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    

 

Q10

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