Acceleration and Retardation - UNSOLVED PRACTICE SET

Q7. Define acceleration. Write its formula and state whether it is a scalar or vector quantity.

Q8. What is retardation? How is it represented mathematically? Give one example from real life where an object undergoes retardation.

Q9. A bus increases its speed from 20 m/s to 35 m/s in 5 seconds, then decreases its speed back to 20 m/s in 3 seconds. Calculate the acceleration in each phase.

Q10. Can an object have zero velocity but non-zero acceleration? Can it have non-zero velocity but zero acceleration? Give one example for each case.

Q11. What does a negative value of acceleration indicate? Give two real-life examples — one from Indian road transport and one from sports.

Q12. Distinguish between uniform acceleration and non-uniform acceleration with one example each. How does the velocity–time graph differ between the two?

Q13. A DRDO test vehicle starts from rest and reaches a speed of 180 m/s in just 12 seconds during a trial run. It then maintains this speed for 30 seconds before braking to a halt in 18 seconds.
(a) Calculate the acceleration during phase 1.
(b) State the acceleration during phase 2.
(c) Calculate the retardation during phase 3.
(d) Describe the velocity–time graph for the entire journey.
(e) What is the significance of the area under the velocity–time graph? 

Q14. Explain the concept of uniform and non-uniform acceleration.
(a) Define each with an example.
(b) A freely falling object near Earth has uniform acceleration of g = 10 m/s². Starting from rest, calculate its velocity at t = 1, 2, 3, and 4 seconds.
(c) Draw (or describe) the velocity–time graph for this free fall.
(d) What does the increasing slope tell you about the motion?

Q15. (a) What is the difference between acceleration and retardation?
(b) Can a body have centripetal acceleration even at constant speed? Explain.
(c) An object thrown horizontally has zero vertical velocity initially but gravity gives it vertical acceleration g = 10 m/s² downward. Simultaneously it moves horizontally at constant 15 m/s. What is happening to its horizontal acceleration? Explain the combined motion qualitatively.

Q16. A Rajdhani Express increases its speed from 0 to 90 km/h in 5 minutes.
(a) Convert 90 km/h into m/s.
(b) Calculate the acceleration of the train in m/s².
(c) If the same acceleration is maintained, what will the speed be after a further 3 minutes?

Q17. A cricket ball is bowled at 36 m/s and the batsman hits it back at 30 m/s in the opposite direction. The ball was in contact with the bat for 0.01 seconds.
(a) What is the change in velocity of the ball? (Hint: consider direction.)
(b) Calculate the acceleration of the ball during contact.
(c) Is this acceleration or retardation? Justify.

Q18. A velocity–time graph shows a straight line starting at v = 20 m/s at t = 0 and ending at v = 0 at t = 8 s.
(a) What type of motion does this represent?
(b) Calculate the acceleration (retardation).
(c) Calculate the distance covered using the area under the graph.
(d) Verify your distance using the equation v² = u² + 2as.