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 moving 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 = ∆v/t to ∆v = at
2. Substitute ∆v = (v - u) to get v - u = at 3. Rearrange to get v = u + at

Question 15

Derive s = (u + v) t / 2

Answer 15

1. Average velocity is given by vavg = (v + u) / 2
2. Displacement is given by s = s0 + vavgt
3. Substitute in the formula for vavg to get
   s = s0 + (v + u) t / 2
4. If the initial displacement (s0) is 0, the formula becomes s = (v + u) 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 v2 = u2 + 2as

Answer 17

1. Square (v = u + at) to get v2 = u2 + 2uat + a2t2
2. Rearrange s = ut + 1⁄2at2 to get at2 = 2s - 2ut
3. Substitute at2 into the first stage to get
   v2 = u2 + 2uat + a (2s - 2ut)
4. Simplify to get v2 = u2 + 2uat + 2as - 2uat
5. Simplify further to get v2 = u2 + 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 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 strength (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 become 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 = 10cos(30)
= 8.7

y = 10sin(30)
= 5

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
formulae can be applied.