A car accelerates uniformly from 18 km/h to 36 km/h in 5 seconds. Calculate its acceleration.
From NCERTAsked by Anonymous24 Oct 2026, 12:19 PM ISTUpdated
The answer
The car's acceleration is 1 m/s².
On the board
A car accelerates from 18 km/h to 36 km/h in 5 seconds. We are to find its acceleration.
a = \frac{v - u}{t}
First, write the formula for acceleration as change in velocity divided by time taken.
u = 18\,\text{km/h}
Write the initial velocity in km/h.
u = 5\,\text{m/s}
checked
Convert the initial velocity to m/s.
v = 36\,\text{km/h}
Write the final velocity in km/h.
v = 10\,\text{m/s}
checked
Convert the final velocity to m/s.
t = 5\,\text{s}
Write the time taken.
a = \frac{10\,\text{m/s} - 5\,\text{m/s}}{5\,\text{s}}
checked
Substitute the values into the formula.
a = 1\,\text{m/s}^2
checked
Calculate the value to find the acceleration.
Answer
a = 1\,\text{m/s}^2
The acceleration of the car is 1 metre per second squared.
Every ticked line was worked again and checked by the computer (SymPy 1.11.1 with units).
Why each step works
Formula: Acceleration (a) is the change in velocity (final minus initial) divided by the time taken. This tells us how quickly the car’s speed is changing every second.
Initial velocity (u): The car starts at 18 km/h. We need to know where it began.
Convert u to m/s: Physics formulas use meters per second (m/s), not km/h. To convert, multiply by 5/18. So, 18 km/h × 5/18 = 5 m/s.
Final velocity (v): The car speeds up to 36 km/h. This is the speed at the end.
Convert v to m/s: Again, convert to m/s. 36 km/h × 5/18 = 10 m/s.
Time (t): The car takes 5 seconds to speed up. This is the time interval for the change.
Substitute values: Put the numbers into the formula: a = (10 m/s – 5 m/s) / 5 s.
Calculate: 10 – 5 = 5. 5 ÷ 5 = 1. So, acceleration a = 1 m/s².
Converting km/h to m/s
Multiply the speed in km/h by 5/18
Example: 18 km/h × 5/18 = 5 m/s
Check your answer
Did you convert km/h to m/s by multiplying by 5/18?
Did you subtract the initial speed from the final speed?
Did you divide by the correct time (5 seconds)?
If yes, your answer should be 1 m/s².
Common mistakes
Forgetting to convert km/h to m/s: Always use m/s in physics calculations.
Mixing up initial and final velocity: Subtract initial from final, not the other way.
Dividing by the wrong time: Use the total time for the change, not per hour or minute.
Try one yourself
A scooter speeds up from 10 km/h to 25 km/h in 3 seconds. What is its acceleration? (Remember to convert km/h to m/s!)
The formula
a = \frac{v - u}{t}
aacceleration (m/s²)
vfinal velocity (m/s)
uinitial velocity (m/s)
ttime taken (s)
Check yourself
Why do we convert km/h to m/s in physics calculations?
Because standard physics units are meters and seconds, so formulas work correctly.
What would happen if you forgot to convert km/h to m/s?
Your answer would be wrong because the units would not match.
If a car goes from 0 to 20 m/s in 4 seconds, what is its acceleration?
5 m/s², because (20 - 0) / 4 = 5.
Quick recap
Always convert speeds from km/h to m/s before using formulas.
Acceleration is the change in velocity divided by time.
Subtract initial speed from final speed, then divide by time.
