Motion in One dimension
Numericals Part:2
Question:1
A body starts from rest with a uniform acceleration of 2 m/s². Find the
distance covered by the body in 2 s.
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2 m/s²
Time (t) = 2 s
Formula:
s = ut + 1/2 at²
Substitution:
= (0 × 2) + 1/2 × 2 × (2)²
Calculation:
=0+1×4
=4m
Final Answer:
Distance covered by the body = 4 m
Question:2
A body starts with an initial velocity of 10 m/s and acceleration 5 m/s². Find
the distance covered in 5 s.
Given:
Initial velocity (u) = 10 m/s
Acceleration (a) = 5 m/s²
Time (t) = 5 s
,Formula:
s = ut + 1/2 at²
Substitution:
= (10 × 5) + 1/2 × 5 × (5)²
Calculation:
= 50 + 1/2 × 5 × 25
= 50 + 2.5 × 25
= 50 + 62.5
= 112.5 m
Final Answer:
Distance covered = 112.5 m
Question:3
A vehicle is accelerating on a straight road. Its velocity at any instant is 30
km/h. After 2 s, it is 33.6 km/h and after further 2 s, it is 37.2 km/h. Find the
acceleration of the vehicle in m/s². Is the acceleration uniform?
Given:
Initial velocity = 30 km/h
Velocity after 2 s = 33.6 km/h
Velocity after next 2 s = 37.2 km/h
Time interval = 2 s
Conversion:
1 km/h = 5/18 m/s
30 × 5/18 = 8.33 m/s
33.6 × 5/18 = 9.33 m/s
37.2 × 5/18 = 10.33 m/s
First 2 seconds:
Formula:
Acceleration (a) = (v - u) / t
Substitution:
= (9.33 - 8.33) / 2
, Calculation:
=1/2
= 0.5 m/s²
Next 2 seconds:
Formula:
Acceleration (a) = (v - u) / t
Substitution:
= (10.33 - 9.33) / 2
Calculation:
=1/2
= 0.5 m/s²
Since the acceleration is the same in both intervals, the acceleration is
uniform.
Final Answer:
Acceleration of the vehicle = 0.5 m/s²
Yes, the acceleration is uniform.
Question:4
A body initially at rest starts moving with a constant acceleration of 2 m/s².
Calculate:
1. The velocity acquired
2. The distance travelled in 5 s
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2 m/s²
Time (t) = 5 s
1. Velocity Acquired
Formula:
v = u + at
Substitution:
Numericals Part:2
Question:1
A body starts from rest with a uniform acceleration of 2 m/s². Find the
distance covered by the body in 2 s.
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2 m/s²
Time (t) = 2 s
Formula:
s = ut + 1/2 at²
Substitution:
= (0 × 2) + 1/2 × 2 × (2)²
Calculation:
=0+1×4
=4m
Final Answer:
Distance covered by the body = 4 m
Question:2
A body starts with an initial velocity of 10 m/s and acceleration 5 m/s². Find
the distance covered in 5 s.
Given:
Initial velocity (u) = 10 m/s
Acceleration (a) = 5 m/s²
Time (t) = 5 s
,Formula:
s = ut + 1/2 at²
Substitution:
= (10 × 5) + 1/2 × 5 × (5)²
Calculation:
= 50 + 1/2 × 5 × 25
= 50 + 2.5 × 25
= 50 + 62.5
= 112.5 m
Final Answer:
Distance covered = 112.5 m
Question:3
A vehicle is accelerating on a straight road. Its velocity at any instant is 30
km/h. After 2 s, it is 33.6 km/h and after further 2 s, it is 37.2 km/h. Find the
acceleration of the vehicle in m/s². Is the acceleration uniform?
Given:
Initial velocity = 30 km/h
Velocity after 2 s = 33.6 km/h
Velocity after next 2 s = 37.2 km/h
Time interval = 2 s
Conversion:
1 km/h = 5/18 m/s
30 × 5/18 = 8.33 m/s
33.6 × 5/18 = 9.33 m/s
37.2 × 5/18 = 10.33 m/s
First 2 seconds:
Formula:
Acceleration (a) = (v - u) / t
Substitution:
= (9.33 - 8.33) / 2
, Calculation:
=1/2
= 0.5 m/s²
Next 2 seconds:
Formula:
Acceleration (a) = (v - u) / t
Substitution:
= (10.33 - 9.33) / 2
Calculation:
=1/2
= 0.5 m/s²
Since the acceleration is the same in both intervals, the acceleration is
uniform.
Final Answer:
Acceleration of the vehicle = 0.5 m/s²
Yes, the acceleration is uniform.
Question:4
A body initially at rest starts moving with a constant acceleration of 2 m/s².
Calculate:
1. The velocity acquired
2. The distance travelled in 5 s
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = 2 m/s²
Time (t) = 5 s
1. Velocity Acquired
Formula:
v = u + at
Substitution:
