Kinematics

Question 1

Explain a parabolic displacement-time graph? Gradient and what that can work out?

Answer 1

The graph shows how the displacement of a particle travelling in a straight line changes with time. The gradient = velocity and working out multiple gradients can determine if it’s accelerating. If the acceleration is constant the graph will be parabolic

Question 2

What are the 4 TUVAX equations?

Answer 2

V = u + at
X = 1/2 (u+v) t
X = ut + 1/2 at^2
V^2 = u^2 + 2ax

Question 3

Derive v = u + at

Answer 3

Acceleration = change in velocity/time

A = v-u/t
⬇️
V = u + at

Question 4

Derive x = 1/2 (u+v) t

Answer 4

Graphically we can show a trapezium and the area under the graph of a trapezium ;
1/2 (a+b) h

So therefore;
X = 1/2 (v+u) t

Question 5

Derive x = ut + 1/2 at^2

Answer 5

By substituting 1 into 2;

X = 1/2 (u+(u + at)) t
X = 1/2 (2ut + at^2)

X = ut + 1/2 at^2

Question 6

Derive v^2 = u^2 + 2ax

Answer 6

By making t the subject of 1 and substituting it into 2;

T = v-u/t
X = 1/2 (u+v) (v-u/a)
2ax = (u+v) (u-v)

V^2 = u^2 + 2ax

Question 7

What equation do you use if working out a horizontal component?

Answer 7

X = V x T

Question 8

Explain what happens when Air is taken into account?

Answer 8

When we take into account Air, acceleration is non-uniform and reduces to zero as the object gains speed

Question 9

Explain terminal velocity?

Answer 9

At the beginning the vertical speed is zero, so no air resistance.
There’s a downward resultant force created by weight so the skydiver accelerates downwards.
As the speed increases they push downwards onto air molecules with increasing force. So the Air molecules are creating an upward force on the skydiver that increases with speed.
Eventually the Air resistance becomes equal to the weight so terminal velocity is reached

Question 10

Explain the four parts to a displacement time graph

Answer 10

Constant acceleration - curve going up
Constant velocity - straight diagonal line
Constant deceleration - curve going down
Stationary - flat line above 0m

Question 11

Explain the four parts to an acceleration time graph

Answer 11

Constant acceleration - box above 0ms-2
Constant velocity - flat line on 0ms-2
Constant deceleration - box below 0ms-2
Stationary - flat line on 0ms-2

Question 11

Explain the four parts to a velocity time graph giving the area under the graph and gradient

Answer 11

Constant acceleration - straight diagonal line (+ direction)
Constant velocity - straight line above 0ms-1
Constant deceleration - straight diagonal line (- direction)
Stationary - flat line on 0ms-1
Area under graph - displacement
Gradient - acceleration - change in velocity/time