1.1. A particle moves in a straight line with a constant acceleration, a. The initial velocity of the particle at t = 0 is u.  After a further time t, its velocity has increased to v. 

(i) Using the definition of acceleration, show that 

$v=u+at$

[2]

(ii) Using the definition of average velocity, show that 

$s=ut+\frac{1}{2}a{t}^{2}$

[3]

(iii) Using these two equations, show that 

${v}^{2}={u}^{2}+2as$

[3]

1.2. A student investigates the motion of a light ball bearing as it falls from rest alongside a vertical 100 cm scale.

The student sets up a camera to take flash photographs of the ball at 0.05 s intervals, as shown in Fig. 1.1.

The first photograph is taken at time t = 0.

Using Fig. 1.1, describe and explain the motion of the ball 

(i) in the interval t = 0 to t = 0.35 s

[2]

(ii) in the interval t = 0.35 to t = 0.55 s.

[2]

1.3. The 100 cm scale is suspended 160 cm above the ground.

Determine the total time of flight for the ball after it is dropped from the starting point of the 100 cm scale.

1.4. The student repeats the experiment with a lead sphere that falls with constant acceleration and does not reach a constant speed.

Determine the number of photographs, including the photograph at t = 0, that will be observed against the 100 cm scale.