## Kinematics

## Constant speed and constant velocity

Contents

- Constant speed and constant velocity

Kinematics is the study of motion without reference to force or mass. The terms involved and their symbols are:

A, acceleration

u, initial velocity

v, final velocity

s, distance travelled or displacement

t, time taken or elapsed

**Constant speed and constant velocity**

Constant speed occurs when there is no acceleration, e.g. if a car is travelling at a speed of 50km/h then after each hour the car will have travelled 50km and a total distance travelled will be given by:

*Distance = speed x time taken*

Velocity is speed in a given direction. For instance, if the car is travelling at 50km/h due east then it would be a velocity and not a speed that is stated.

Similar to the above if the velocity remains constant, i.e. no acceleration or deceleration, then the distance travelled will be given by:

*Distance in a particular direction = velocity x time taken*

*or s = v x t (or s = vt)*

This section of work will only be considering motion in a straight line, i.e. linear motion, and therefore velocity will be in one of two directions denoted by positive or negative values.

For example if motion to the right is considered to be positive, then:

-> 10m/s will be denoted by + 10m/s or simply 10m/s

<- 10m/s will be denoted by -10m/s

**Units**

As can be seen from the above different units can be used for distance, velocity and time.

**Example 1: **Convert 50km/h to m/s.

1 km = 1000 m and 1 h = 3600 s

Therefore

50 km/h = 50x 1000

3600

= 13.9 m/s

Note: to convert from km/h to m/s divide by 3.6. Similarly to convert from m/s to km/h multiply by 3.6

**Example 2:**

A cyclist has a velocity of 12 km/h. Determine the distance travelled in 7minutes and the time taken to travel 425m.

First convert 12km/h to m/min

12 km/h = 12 x 1000/60 m/min

=200 m/min

Apply s = vt to calculate the distance travelled in 7 minutes.

S = 200 x 7

= 1400m or 1.4km

Apply s = vt to calculate the time taken to travel 425m.

425 = 200 x t

t = 425/200

= 2.125 min

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