Unit 1.2) Kinematics

Question 1

Define Mean speed, the equation used to calculate mean speed, and the respective SI units.

Answer 1

Mean speed is defined as the average rate of change of distance.
The equation used is:
mean speed = total distance/total time taken and the SI units are m s^-1

Question 2

What is meant by instantaneous speed?

Answer 2

The speed of an object at a given point in time.

Question 3

Define displacement

Answer 3

The displacement of an object is the shortest distance between its initial and final position, together with the direction.

Question 4

Define velocity, the equation used to calculate velocity, and the respective SI units

Answer 4

The velocity of an object is defined as the rate of change of displacement , or speed in a given direction, making velocity a vector.
The equation used is velocity = Change in displacement/ time and the SI units are ms^-1

Question 5

What is the difference between mean velocity and instantaneous velocity?

Answer 5

Mean velocity is the average velocity of an object over a specified period of time, whereas instantaneous velocity is the velocity of the object at a given point in time. ( This difference between mean and instantaneous applies to speed and acceleration as well.

Question 6

Define acceleration, the equation used to calculate acceleration, and the respective SI units.

Answer 6

Acceleration is defined as the rate of change of velocity, making it a vector.
The equation used is acceleration = change in velocity/time and the SI units are ms^-2.

Question 7

What does a straight, horizontal line represent on a displacement time graph?

Answer 7

A stationary object

Question 8

What does a line with a constant, non zero gradient represent on a displacement -time graph?

Answer 8

An object moving with constant velocity.

Question 9

What does a curved line represent on a displacement-time graph?

Answer 9

Acceleration(if gradient is increasing) or deceleration(if gradient is decreasing)

Question 10

What does a straight, horizontal line represent on a velocity-time graph?

Answer 10

An object with constant velocity

Question 11

What does a line with a constant, non-zero gradient represent on a velocity-time graph?

Answer 11

An object that is accelerating(positive gradient)or decelerating(negative gradient).

Question 12

What does the area under a velocity -time graph represent?

Answer 12

Displacement

Question 13

What does the area under an acceleration-time graph represent?

Answer 13

Velocity

Question 14

Derive v = u + at

Answer 14

1. Rearrange a = Δv/t to Δv = at
2. substitute Δv = (v-u) to get v-u = at
   3.Rearrange to get v = u + at

Question 15

Derive s = (u+v)/2 t

Answer 15

1.Average velocity is given by v = (v+U) / 2
2.Displacement is given by S = S + vt
3.Substitute in the formula for v(average) to get S = S + (v + u) t/2
4.If the initial displacement (Second S) is 0, the formula becomes s =(u+v)t/2

Question 16

Derive s = ut + 1/2at^2

Answer 16

1.Substitute v = u + at into S = (u+v) t/2 to get S = (u+(u+at))t/2
2.Simplify to S = (2u + at)t/2
3.Expand and Simplify to S = ut + 1/2at^2

Question 17

Derive v^2 = u^2 + 2as

Answer 17

1.Square(v = u+at) to get v^2 = u^2 + 2uat + a^2t^2
2.Rearange s = ut + 1/2at^2 to get at^2 = 2s - 2ut
3.Substitute at^2 into the first stage to get, v^2 = u^2 + 2uat + a(2s - 2ut)
4.Simplify to get v^2 = u^2 + 2uat + 2as - 2uat
5.Simplify further to get v^2 = u^2 + 2as

Question 18

What can be described as ‘the change in displacement per unit time’.

Answer 18

Velocity.
Instantaneous velocity can be found by measuring the gradient of a tangent to a displacement time-time graph.

Question 19

What is the area under a velocity time and acceleration-time graph?

Answer 19

The displacement and the velocity respectively.

Question 20

As speed increases, air resistance…

Answer 20

Increases(proportional to the square of the speed).

Question 21

A ball is projected off a castle at 6m/s. How does its horizontal velocity change from its launch until it hits the ground?

Answer 21

The horizontal velocity remains the same as there is no acceleration in that direction.

Question 22

How do the SUVAT equations reflect that all objects fall at the same rate?

Answer 22

Mass is not included in the SUVAT equations, showing that the mass of an object does not affect its speed or acceleration. Therefore, all objects fall at the same rate regardless of their masses.

Question 23

In projectile motion, what is the vertical acceleration?

Answer 23

The vertical acceleration is equal to the gravitational field (g) towards the centre of the Earth

Question 24

What is meant by terminal velocity?

Answer 24

When the forces acting on the falling object becomes balanced, the acceleration becomes zero and the object is moving at maximum velocity.

Question 25

A ball is fired at a velocity of 10m/s, at an angle of 30 to the horizontal. Find the vertical and horizontal components of velocity.

Answer 25

X = 10 cos 30 = 8.7 m/s
y = 10 sin 30 = 5 m/s

Question 26

Describe bodies falling in gravitational fields with air resistance.

Answer 26

Air resistance increases with speed, so as a body accelerates, the resistance increases.
Acceleration decreases as speed increases.
When air resistance and weight are equal, the body is falling with its terminal velocity.
SUVAT does not account for air resistance.

Question 27

Describe bodies falling in gravitational fields without air resistance.

Answer 27

Resultant force is only weight.
Acceleration = g.
The acceleration is constant so SUVAT formula can be applied.