Motion – Easy Step-by-Step Solutions
TWO MARK QUESTIONS
1. Two differences between instantaneous speed and instantaneous velocity
Instantaneous speed is the speed at a particular instant and is a scalar quantity.
Instantaneous velocity is the velocity at a particular instant and is a vector quantity.
2. Position-time graph for constant speed
The graph is a straight line with constant slope.
3. Position-time graph for positive direction with negative acceleration
The graph is a curve with decreasing slope.
4. Average velocity and uniform velocity
Average velocity = Total displacement / Total time.
Uniform velocity means equal displacement in equal intervals of time in the same direction.
5. Velocity after 20 s
Given:
u = 5 m/s, a = 1 m/s², t = 20 s
v = u + at
= 5 + (1 × 20)
= 25 m/s.
6. Velocity-time graph explanation
(i) Ball thrown upward: velocity decreases to zero and becomes negative while returning.
(ii) Ball dropped and bouncing: velocity increases downward and changes direction after collision.
7. Ball thrown downward
Initial speed = 20 m/s.
After collision speed becomes 18 m/s.
Using:
v² = u² - 2gh
0 = 18² - 2 × 9.8 × h
h = 324 / 19.6
h = 16.53 m.
THREE MARK QUESTIONS
1. Derive v = u + at
a = (v - u)/t
at = v - u
v = u + at.
2. Derive S = ut + 1/2at²
Average velocity = (u + v)/2
S = [(u + v)/2] × t
Using v = u + at,
S = ut + 1/2at².
3. Derive v² - u² = 2as
Using:
v = u + at and S = [(u+v)/2]t
After substitution:
v² - u² = 2as.
