{"id":6,"date":"2014-11-19T08:58:38","date_gmt":"2014-11-19T08:58:38","guid":{"rendered":"http:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/velocity-and-displacement-%e2%80%94-vectors-and-scalars\/"},"modified":"2014-11-19T09:20:21","modified_gmt":"2014-11-19T09:20:21","slug":"velocity-and-displacement-%e2%80%94-vectors-and-scalars","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/velocity-and-displacement-%e2%80%94-vectors-and-scalars\/","title":{"rendered":"Velocity and displacement \u2014 vectors and scalars"},"content":{"rendered":"

Vector and Scalar Quantities<\/span><\/strong><\/p>\n

\u00a0<\/span><\/strong><\/p>\n

A scalar quantity<\/strong> is fully described by its magnitude (size) and unit, e.g.<\/p>\n

\"\"<\/a><\/p>\n

A vector quantity <\/strong>is fully described by its magnitude, unit, and direction, <\/strong>e.g.<\/p>\n

\"\"<\/a><\/p>\n

Distance and Displacement<\/span><\/strong><\/p>\n

Distance <\/strong>is a scalar<\/strong> quantity.\u00a0 <\/strong>It measures the total distance travelled, no matter in which direction.<\/p>\n

Displacement <\/strong>is a vector<\/strong> quantity.\u00a0 It is the length measured from the starting point to the finishing point in a straight line. Its direction<\/strong> must be stated.<\/p>\n

Example<\/em><\/strong><\/p>\n

A girl walks 3 km due north then turns and walks 4 km due east as shown in the diagram.<\/em><\/p>\n

\"\"<\/a><\/em><\/p>\n

Calculate<\/p>\n

(a)\u00a0 The total distance travelled
\n(b)\u00a0 \u00a0The girl\u2019s final displacement relative to her starting position.<\/p>\n

Solution<\/em><\/strong><\/p>\n

(a)\u00a0 <\/em>Total distance \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 3 km + 4 km<\/em>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 7 km<\/em><\/p>\n

(b)\u00a0 <\/strong>(to calculate displacement, we need to draw a vector diagram)<\/em><\/strong>\u00a0<\/strong><\/p>\n

(this solution involves using Phythagoras and trig functions (SOH-CAH=TOA), but you can also solve these types of problems using a scale diagram).<\/em><\/strong><\/p>\n

\"\"<\/a>\u00a0<\/em><\/strong><\/p>\n

Speed and Velocity<\/span><\/strong><\/p>\n

Speed is a scalar<\/strong> quantity.\u00a0 As discussed above, speed is the distance<\/strong> travelled per unit time.<\/p>\n

\"\"<\/a><\/p>\n

Velocity is a vector <\/strong>quantity (the vector equivalent of speed). Velocity is defined as the displacement <\/strong>per unit time.<\/p>\n

\"\"<\/a><\/p>\n

Since velocity is a vector, <\/strong>you must <\/strong>state its direction.\u00a0<\/p>\n

The direction of velocity will be the same as the displacement. <\/strong><\/p>\n

Example<\/em><\/strong><\/p>\n

The girl\u2019s walk in the previous example took 2.5 hours.<\/p>\n

Calculate<\/p>\n

(a)\u00a0 The average speed
\n(b)\u00a0 The average velocity for the walk, both in km\/h<\/p>\n

Solution<\/em><\/strong><\/p>\n

\"\"<\/a>(a)\u00a0\u00a0 <\/em>Distance = 7 km\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>\u00a0<\/em>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Time = 2.5 hours<\/em><\/p>\n

\u00a0<\/em>\u00a0<\/p>\n

\u00a0<\/em>\u00a0<\/p>\n

\u00a0<\/em>\u00a0<\/p>\n

\"\"<\/a><\/em><\/p>\n

\u00a0<\/em><\/p>\n

(b)\u00a0\u00a0 <\/em>Displacement = 5 km (053\u02da)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>\u00a0<\/em>
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Time = 2.5 hours<\/em><\/p>\n

\u00a0<\/em>\u00a0<\/em>
\n\u00a0<\/em><\/strong><\/p>\n

\u00a0<\/em><\/strong><\/p>\n

\u00a0<\/em><\/strong><\/p>\n

(When performing calculations on speed and velocity like the above, it is best to write the equations in words as shown, to avoid confusion with symbols.\u00a0 This communicates your understanding in the clearest way).<\/em><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Vector and Scalar Quantities \u00a0 A scalar quantity is fully described by its magnitude (size) and unit, e.g. A vector quantity is fully described by its magnitude, unit, and direction, e.g. Distance and Displacement Distance is a scalar quantity.\u00a0 It measures the total distance travelled, no matter in which direction. Displacement is a vector quantity.\u00a0 … Continue reading “Velocity and displacement \u2014 vectors and scalars”<\/span><\/a><\/p>\n","protected":false},"author":2454,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-6","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/pages\/6","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/users\/2454"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/comments?post=6"}],"version-history":[{"count":11,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/pages\/6\/revisions"}],"predecessor-version":[{"id":30,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/pages\/6\/revisions\/30"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/hyndsecphysn5s4\/wp-json\/wp\/v2\/media?parent=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}