Equations of motion numericals: Class 9 practice
For uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Speed and velocity
- SI units
The idea behind equations of motion numericals
For uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as. Choose the equation that contains the three known quantities and the one you need.
Step-by-step method
- List u, v, a, s, t with units (SI).
- Choose the equation without the quantity you neither know nor need.
- Substitute and solve.
- Retarding motion has negative a.
Worked example 1 (Basic)
A car starts at 6 m/s and accelerates uniformly at 1 m/s² for 3 s. Find its final velocity.
- v = u + at = 6 + 1 × 3
- v = 9 m/s
- Answer: 9 m/s
Worked example 2 (Standard)
A cyclist moving at 12 m/s accelerates at 2 m/s² for 5 s. How far does she travel in this time?
- s = ut + ½at² = 12 × 5 + ½ × 2 × 5²
- s = 85 m
- Answer: 85 m
Worked example 3 (Challenge)
A train moving at 26 m/s brakes uniformly and stops in 133 m. Find its retardation.
- v² = u² + 2as with u = 26, v = 0
- 0 = 676 + 2a × 133
- a = −2.54 m/s²
- Answer: 2.54 m/s² (retardation)
Common mistakes and misconceptions
- Using km/h without converting to m/s
- Positive a for a braking vehicle
Practice questions
- (Basic) A car starts at 4 m/s and accelerates uniformly at 1 m/s² for 5 s. Find its final velocity.
- (Basic) A car starts at 18 m/s and accelerates uniformly at 5 m/s² for 3 s. Find its final velocity.
- (Standard) A cyclist moving at 10 m/s accelerates at 1 m/s² for 4 s. How far does she travel in this time?
- (Standard) A cyclist moving at 16 m/s accelerates at 1 m/s² for 8 s. How far does she travel in this time?
- (Challenge) A train moving at 47 m/s brakes uniformly and stops in 206.5 m. Find its retardation.
- (Challenge) A train moving at 28 m/s brakes uniformly and stops in 147 m. Find its retardation.
Answer key with full working
- Q1: v = u + at = 4 + 1 × 5 → v = 9 m/s → Answer: 9 m/s
- Q2: v = u + at = 18 + 5 × 3 → v = 33 m/s → Answer: 33 m/s
- Q3: s = ut + ½at² = 10 × 4 + ½ × 1 × 4² → s = 48 m → Answer: 48 m
- Q4: s = ut + ½at² = 16 × 8 + ½ × 1 × 8² → s = 160 m → Answer: 160 m
- Q5: v² = u² + 2as with u = 47, v = 0 → 0 = 2209 + 2a × 206.5 → a = −5.35 m/s² → Answer: 5.35 m/s² (retardation)
- Q6: v² = u² + 2as with u = 28, v = 0 → 0 = 784 + 2a × 147 → a = −2.67 m/s² → Answer: 2.67 m/s² (retardation)
Syllabus note
This skill is listed under "Motion" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is equations of motion numericals in?
"Motion", Class 9 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.