UNIT 6: MOTION

1-Basic concepts: trajectory, reference frame, distance travelled, displacement, speed, average speed, acceleration.

2-Uniform rectilinear motion: graphs, motion equations and problems.

3-Uniformly accelerated rectilinear motion: graphs, motion equations and problems.

UNIFORM RECTILINEAR MOTION (URM)

The trajectory is rectilinear (it means the moving object describes a straight line).
The speed is constant.

Data

A- Every second the car travels 10 m. It means its speed is constant.

v= 10m/s

B- Every second the car travels 20 m. It means its speed is constant.

v= 20 m/s

position vs time graphs

In URM, the position vs time graph is always a straight line. The slope is related to the speed.

The speed in motion B is greater that the speed in motion A. We can deduce this from the graph because the steeper the line, the greater the speed.

Every second, the person is travelling 4 metres. The speed is 4 m/s

The person is moving leftwards, approaching to x=0

speed vs time graphs

A and B show how speed changes over time for the data shown above.

In URM speed-time graph is always a straight line parallel to the x-axis (time axis)

Problems on uniform rectilinear motion (URM)

Para estos problemas, hay que usar tres ecuaciones, las que relacionan las tres variables; velocidad, distancia recorrida y tiempo empleado. En este vídeo os cuento un truquito para aprender a deducirlas fácilmente. Cuando la velocidad no es constante, podemos sustituir velocidad por "velocidad media" en el triángulo.

EXERCISES ON URM

1) If it takes 3 hours to drive a distance of 192 km on a motorway, what would be your average speed in km/h?

2) Jorge decided to cycle to his friend's house at a speed of 5km/h. It took him 30 minutes to get there. How far was his friend's house?

3) If you drive at 100 km/h, how long would it take you to travel a distance of 250 km?

4) A bus travels at 50 km/h on a straight road. How long will it take for the bus to travel 150 km?

5) Fernando's car travels a distance of 350 km in 2 h. Consider the speed was kept constant for the whole journey and calculate it. Sol: 175km/h

6) Your aunt is walking her dog. They walk a distance of 300 m in 60 s. What was their speed in m/s? Sol: 5m/s

7) Eduardo has robbed a bank. His getaway car drives a distance of 60 km at a speed of 120 km/h. How long did his journey take?

Sol: 0.5 h or 30 min

8) Emma and two friends of hers are going to a party together. They walk at a speed of 3 m/s for 200 s. How far away is the party? Sol: 600 m

9) Pablo and Elena have got married. After the wedding, a horse carriage picks them up and take them to a beautiful park. If it was 2 km away and took them 5 minutes to get there, what was the speed in m/s? Consider the motion was uniform. Sol: 7m/s (approx.)

10) Julia is cycling to the supermarket to buy some groceries. If it takes her 10 minutes to get there and she rode at 6 m/s, how far is the supermarket? Sol: 3600m

11) Determine the time taken for a girl, riding her bike at 3 m/s, to travel 2400 m. Sol: 800 s

12) How far will Pedro travel in 15 minutes, driving his motorcycle at 24 m/s? Express your answer in metres. Sol: 21600m (21.6 km)

13) Two cars leave the petrol station at the same time in opposite direction. How far apart will they be in 30 minutes if one travels at 20 m/s and the other one at 35 m/s?

14) Sara and Blanca are in Physical Education class. They are 20 metres apart. Then, they start running at the same time in opposite directions at 6 m/s and 5 m/s respectively. How long will it take them to meet?

UNIFORMLY ACCELERATED RECTILINEAR (UARM)

The trajectory is rectilinear (it means the moving object describes a straight line).
The speed is not constant but it changes (increases or decreases) gradually; for example, it increases 2 m/s every second. The change of the speed in each unit of time is called acceleration.
The acceleration is constant.

Calculating acceleration from the data:

A- Every second speed increases by 1m/s. It means that the acceleration is 1m/s2.

B- Every second speed increases by 2 m/s. It means that the acceleration is 2m/s2.

C-Every second speed decreases by 2m/s. It means that the acceleration is -2m/s2.

Calculating acceleration from v-t graphs:

A and B are UARM. It means the speed increases gradually. The acceleration in B is greater that in A because the steeper the line, the greater the acceleration.

A: from t=3s to t=6s v changes from 3m/s to 6m/s

a= (vf -vi)/(tf-ti)= (6m/s-3m/s)/(6s-3s) = 1m/s2

B: a=2m/s2

C : it is also a UARM but, in this motion, speed decreases gradually.

a= -2m/s2.

The slope of a speed versus time graph tells us the object's acceleration

position vs time graph

In UARM the body doesn't travel the same distance per unit of time.

The position-time graph for UARM is not a straight line but a curved line called "parabola" as shown at the left.

The data at the left show the position vs time for an UARM with a= 3m/s2

Escoge cómo quieres que se mueve este hombrecillo dándole valores a su posición inicial, su velocidad y su aceleración en este juego

Con este simulador virtual puedes escoger la posición y velocidad inicial de un coche y decidir si tiene o no aceleración. A medida que el coche se va moviendo, se irán construyendo las gráficas posición frente al tiempo, velocidad frente al tiempo y aceleración frente al tiempo. Podrás comprobar cómo, si el movimiento es rectilíneo y uniforme, recorre siempre la misma distancia en el mismo intervalo de tiempo pero si es movimiento rectilíneo uniformemente acelerado, esto no ocurre.

Imagina que vas conduciendo una moto por una carretera y vas variando tu velocidad. Con este simulador virtual, mientras conduces, se va formando la gráfica de la velocidad frente al tiempo.

Problems on uniformly accelerated rectilinear motion (UARM)