# StudySquare

This page covers the following topics:

1. Distance

2. Displacement

3. Area under velocity-time graphs

4. Work done and distance

Distance is defined as how far in total an object has travelled. Distance is a scalar quantity, meaning that it is measured only by magnitude and its direction is insignificant. It is usually measured in metres (m). Kilometres (km) can be used for greater distances, and centimetres (cm) and millimetres (mm) can be used for shorter distances.

Displacement is defined as the total change in position of an object. Displacement is a vector quantity, meaning that it is measured by both magnitude and direction. It is usually measured in metres (m). The same units (m, km, cm, mm) as distance are used to measure displacement.

The motion of an object travelling in a straight line can be modelled using a velocity-time graph, where velocity is the y-axis and time is the x-axis. The area under the graph represents the displacement of the object, whereas the gradient of the graph is the acceleration. When the lines of the graph are straight, simple geometry can be used to calculate the area under the graph and thus the displacement of the object, whereas when the lines of the graph are curved, the technique of counting squares can be used instead.

Work is done when a force causes a body to move. It can be calculated using W = force × distance travelled in direction of force, and has units joules (J). The distance covered by an object can be calculated when the work done on the object and the force being applied to it are known.

# 1

The distance between Mary's house and the bakery is 1.5 km. What will be the total distance travelled if Mary walks to the bakery from her house and back?

total distance = 1.5 km + 1.5 km = 3 km

3 km

# 2

A car takes the route given in the diagram. Explain whether the distance or the magnitude of the displacement will be greater from start to end, and give them in terms of A, B, C, D, E and F.

The total distance travelled by the car will be the sum of all the small components of the journey, whereas the displacement magnitude will only give the direct distance between the start and the end to represent the overall change in position of the car, thus the distance will be greater than the displacement.

distance = A + B + C + D + E + F

displacement magnitude = A + C + E

distance = A + B + C + D + E + F > displacement magnitude = A + C + E

# 3

William goes on a walk of distance 2 km. Is William's displacement also equal to 2 km?

There is not enough information to deduce whether William's displacement is 2 km, since the route of William's walk is unknown. Displacement would be equal to 2 km only if William's walk was a straight line walk of 2 km.

not enough information

# 4

A man is pushing a shopping trolley a horizontal force of 80 N. He pushes the trolley forward at a constant velocity, by doing 160 J of work. Calculate the distance the trolley is pushed through.

d = W/F

d = 160 J/80 N = 2 m

2 m

# 5

Calculate the displacement of the object whose motion is modelled by the given velocity-time graph in the first 5 seconds.

Displacement between t = 0 and t = 5 s is area under the graph in the given interval.

The total number of squares under the graph is 27, thus s = 27 m.

This is an approximate value, as counting squares is only an estimate.

27 m

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