Rate of Change of Velocity – Long Answer Questions
Medium Level (Application & Explanation)
Q1. Differentiate between uniform motion and non-uniform motion. How do they affect the change in velocity? Give suitable examples.
Answer:
In uniform motion, an object moves with a constant velocity.
The change in velocity is zero in equal time intervals.
Example: A car moving steadily at 50 km/h on a straight road.
In non-uniform motion, the velocity changes with time.
The change in velocity is non-zero, and it can be irregular.
Example: A bicycle accelerating from rest to 20 km/h over a distance.
Q2. Define acceleration. Write its formula and SI unit. Explain with a numerical example.
Answer:
Acceleration is the rate of change of velocity with time.
It tells how fast the velocity changes.
Formula: a = (v − u) / t, where v is final velocity, u is initial velocity, t is time.
The SI unit of acceleration is m/s².
Example: A car goes from 20 m/s to 40 m/s in 5 s.
Then, a = (40 − 20)/5 = 4 m/s². This is positive acceleration.
Q3. Explain positive and negative acceleration with real-life cases. Why is negative acceleration also useful?
Answer:
Positive acceleration means velocity increases with time.
Example: A rocket speeding up during launch.
Negative acceleration (or deceleration) means velocity decreases with time.
Example: A cyclist braking to slow down at a turn.
Negative acceleration is useful for safety. It helps us stop in time.
It is still called acceleration, as it is the rate of change of velocity.
Q4. What is uniform acceleration? How is it different from non-uniform acceleration? Give daily-life examples.
Answer:
Uniform acceleration means equal changes in velocity in equal time intervals.
Example: A freely falling object near Earth with 9.8 m/s² acceleration.
Non-uniform acceleration means unequal changes in velocity in equal times.
Example: A car in city traffic, speeding up and slowing down irregularly.
In uniform acceleration, a is constant.
In non-uniform acceleration, a keeps changing with time.
Q5. A scooter increases its velocity from 10 m/s to 25 m/s in 3 s. Calculate the acceleration. Then compare it with a case where it slows from 25 m/s to 10 m/s in 3 s.
Answer:
Given: u = 10 m/s, v = 25 m/s, t = 3 s.
a = (v − u) / t = (25 − 10) / 3 = 5 m/s². This is positive acceleration.
Now, slowing case: u = 25 m/s, v = 10 m/s, t = 3 s.
a = (10 − 25) / 3 = −5 m/s². This is negative acceleration.
The magnitude is the same (5 m/s²), but the sign changes.
Positive means speeding up. Negative means slowing down.
High Complexity (Analysis & Scenario-Based)
Q6. A cyclist starts from rest, reaches 8 m/s in 4 s, and then slows to 5 m/s in the next 3 s. Find the accelerations in both intervals and classify the type of acceleration.
Answer:
First interval: u = 0, v = 8 m/s, t = 4 s.
a₁ = (8 − 0) / 4 = 2 m/s². This is positive acceleration.
Second interval: u = 8 m/s, v = 5 m/s, t = 3 s.
a₂ = (5 − 8) / 3 = −1 m/s². This is negative acceleration.
The acceleration changes between intervals, so it is non-uniform acceleration overall.
The motion shows both speeding up and slowing down phases.
Q7. A roller coaster goes downhill and then climbs uphill. Discuss the nature of acceleration in both parts. Explain signs and changes clearly.
Answer:
On the downhill, the coaster’s speed increases.
The acceleration is in the same direction as velocity. It is positive acceleration.
On the uphill, the coaster slows down.
The acceleration is opposite to velocity. It is negative acceleration.
The magnitude of acceleration may change due to slope and friction.
This makes the overall acceleration non-uniform across the track.
Q8. A car moves at 20 m/s and comes to rest at a red light in 4 s. Calculate the acceleration and explain what it tells about the motion.
Answer:
Given: u = 20 m/s, v = 0 m/s, t = 4 s.
a = (0 − 20) / 4 = −5 m/s².
The negative sign shows deceleration.
The car is slowing down steadily.
Since a is constant here, it is uniform acceleration (negative).
The driver applied brakes and reduced speed smoothly.
Q9. An apple falls freely from a tree. Explain why this is called uniformly accelerated motion. Describe what happens to its velocity every second.
Answer:
A freely falling body near Earth has uniform acceleration.
Its acceleration is about 9.8 m/s² downward.
This means, in each 1-second interval, its velocity increases by ~9.8 m/s.
The change in velocity is the same in equal times.
So the motion is uniformly accelerated even though speed is rising.
The direction of acceleration is constant toward Earth.
Q10. You sprint towards a basketball hoop, then slow down to stop. Describe the acceleration in different phases of your run. Classify each phase.
Answer:
At the start, you speed up from rest.
Acceleration is positive and usually non-uniform as you push harder.
In mid-sprint, your speed may stabilize.
Acceleration becomes near zero if velocity is steady.
As you approach the hoop, you brake to stop.
Acceleration is negative. If braking is steady, it is uniform deceleration.
Q11. A train increases speed from 15 m/s to 30 m/s in 10 s, then keeps the same speed for 20 s, and finally slows to 10 m/s in 5 s. Analyze the acceleration in each phase.
