Speed & Velocity - There Is a Difference!
Speed & Velocity - there is a difference!
If a car takes 10 seconds to travel along a straight road for 300 meters it means that the car travels at an average speed of 30 metres per second…
(30 m/s or 30 ms-1)
Velocity is defined as speed in a particular direction, for example 30ms-1 east, or 60 km/h west.
Vectors and Scalars
Below shows a car travelling at constant speed, however its velocity changes each time it turns a corner, because the direction of its motion changes.
Quantities that do not require a direction to specify them are scalar quantities (e.g. speed & distance).
Quantities that do require a direction to specify them are vector quantities (e.g. acceleration & velocity)
A change in velocity: v = v - u
When adding vectors we must not only consider the magnitude of the vectors but also there direction…
The sum of the vectors is called the resultant vector.
For example, if a car travels 8 km North then 14 km East what is the resultant vector addition?
Acceleration
The velocity of a car increases when it starts moving from rest and decreases when the brakes are applied. Cars can thus speed up (accelerate) and slow down (decelerate).
If the change in velocity is measured in m/s and the time in seconds, then the acceleration is measured in ‘metres per second per second’… m/s2 or ms-2
A car slowing down has a deceleration, or negative acceleration.
Describing Motion
Be careful when analysing speed and velocity… Consider this:
Question
A tennis ball is travelling at 4.0 m/s east. It collides with a wall and rebounds at 2.5 m/s west. If the collision time with the wall is 30 ms, calculate:
a) The change in speed of the ball
b) The change in velocity
c) The average acceleration of the ball during the collision.
Velocity-Time Graphs
Below is a velocity-time graph for a car accelerating uniformly (at constant rate) from rest for a short time. The greater the acceleration the steeper the graph. Thus, acceleration on a graph is determined by the gradient of the graph (gradient = rise/run).
The area under the graph gives the distance travelled, for a v-t graph!
Position-Time Graphs
A position-time (s-t) graph is simply that… It indicates the position of a body, at a certain time, form a ‘start position’. The velocity at a particular time can also be calculated by the gradient. An instantaneous velocity can be found on a curve by the gradient of the tangent.
Acceleration-Time Graphs
An acceleration-time (a-t) graph shows the acceleration of the body at any time. The area under the graph is the change in velocity for the body over the time.
Question
A car with good brakes, but smooth tyres, has a maximum retardation of 2.00 m s–2 on a wet road. The driver has a reaction time of 0.75 s. The driver is travelling at 75.0 km h–1 when she sees a danger and reacts by braking.
a) How far does the car travel during the reaction time?
b) Assuming maximum retardation, calculate the braking time.
c) Determine the total distance travelled by the car from the time the driver realises the danger to the time the car finally stops.
Question
A student is running to catch his bus. The fastest speed he can maintain is 7.0 m s-1. He sees the bus 20 m down the road. It is just pulling away from the kerb. If the bus accelerates away from him at a constant rate of 1.0 m s-2 will the student be able to catch up to the bus?