NCERT Solutions: Motion (Class 9 Science)

Chapter overview

This chapter builds the vocabulary and equations used throughout mechanics: distance, displacement, speed, velocity, acceleration, and the three equations of motion for uniformly accelerated bodies.

Key formulas

• Speed: Speed = Distance / Time
• Velocity: Velocity = Displacement / Time (a vector - has direction)
• Acceleration: a = (v - u) / t, where u is initial velocity and v is final velocity
• Equations of motion (uniform acceleration):
  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as

Worked practice problem 1 — Distance vs displacement

Question: A student walks 4 m east, then 3 m north. Find the total distance travelled and the magnitude of displacement.

Solution:

Distance travelled = 4 + 3 = 7 m (sum of the path lengths)

Displacement is the straight-line distance from start to end point, found using the Pythagorean theorem (since the two legs are perpendicular):

Displacement = √(4² + 3²) = √(16 + 9) = √25 = 5 m

Answer: Distance = 7 m, Displacement = 5 m (directed north-east of the starting point).

Worked practice problem 2 — Equations of motion

Question: A car starts from rest and accelerates uniformly at 2 m/s² for 10 seconds. Find the final velocity and the distance covered.

Solution:

Using v = u + at with u = 0, a = 2, t = 10:

v = 0 + 2(10) = 20 m/s

Using s = ut + ½at²:

s = 0(10) + ½(2)(10²) = 0 + 100 = 100 m

Answer: Final velocity = 20 m/s, distance covered = 100 m.

Worked practice problem 3 — Third equation of motion

Question: A ball moving at 15 m/s decelerates uniformly at 3 m/s² until it stops. Find the distance it travels before stopping.

Solution:

Using v² = u² + 2as with v = 0, u = 15, a = -3:

0 = 15² + 2(-3)s
0 = 225 - 6s
s = 225 / 6 = 37.5 m

Answer: The ball travels 37.5 m before coming to rest.

Common mistakes to avoid

• Treating distance and displacement as always equal - they’re only equal for straight-line motion with no direction change.
• Forgetting to use a negative sign for deceleration when substituting into the equations of motion.
• Mixing up speed (scalar) with velocity (vector) when a question asks specifically for one or the other.

Looking for the official textbook PDF for this chapter? Visit our Class 9 NCERT Books page for the direct download link.