{"id":4,"date":"2016-05-04T11:16:01","date_gmt":"2016-05-04T11:16:01","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/?page_id=4"},"modified":"2016-05-04T11:29:16","modified_gmt":"2016-05-04T11:29:16","slug":"tutorial-1","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/tutorial-1\/","title":{"rendered":"Tutorial 1"},"content":{"rendered":"

<\/h1>\n

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

Equations of motion <\/strong><\/p>\n

 <\/p>\n

1\u00a0\u00a0 The displacement, s in metres, of an object after a time, t in seconds, is given by s = 90t \u2013 4 t2<\/sup><\/p>\n

(a)\u00a0\u00a0 Find by differentiation the equation for its velocity.<\/p>\n

(b)\u00a0\u00a0 At what time will the velocity be zero?<\/p>\n

(c)\u00a0\u00a0 Show that the acceleration is a constant and state its value.<\/p>\n

 <\/p>\n

2\u00a0\u00a0 For an object moving with constant acceleration, show by integration that the velocity, v, is given by v = u + at.<\/p>\n

State clearly the meaning of the symbol, u, in this equation.<\/p>\n

 <\/p>\n

    \n
  1. For a body moving with velocity v = u + at, show by integration that s = ut + \u00bd at2<\/sup>.<\/li>\n<\/ol>\n

    Where the symbols have their usual meaning.<\/p>\n

     <\/p>\n

      \n
    1. The displacement, s, of a moving object after a time, t, is given by s =\u00a0 8 \u2013 10t + t2<\/sup>.<\/li>\n<\/ol>\n

      Show that the unbalanced force acting on the object is constant.<\/p>\n

       <\/p>\n

        \n
      1. The displacement, s, of an object after time, t, is given by s = 3t3<\/sup> + 5t.<\/li>\n<\/ol>\n

        (a)\u00a0\u00a0 Derive an expression for the acceleration of the object.<\/p>\n

        (b)\u00a0\u00a0 Explain why this expression indicates that the acceleration is not constant.<\/p>\n

         <\/p>\n

          \n
        1. A trolley is released from the top of a runway which is 6 m long.<\/li>\n<\/ol>\n

          The displacement, s in metres, of the trolley is given by the expression s = 5t + t2<\/sup>,\u00a0 where t is in seconds.<\/p>\n

          Determine:<\/p>\n

          (a)\u00a0\u00a0 an expression for the velocity of the trolley<\/p>\n

          (b)\u00a0\u00a0 the acceleration of the trolley<\/p>\n

          (c)\u00a0\u00a0 the time it takes the trolley to reach the bottom of the runway<\/p>\n

          (d)\u00a0\u00a0 the velocity of the trolley at the bottom of the runway.<\/p>\n

           <\/p>\n

            \n
          1. A box slides down a smooth slope with an acceleration of 4 m s-2<\/sup>. The velocity of the box at a time t = 0 is 3 m s-1<\/sup> down the slope.<\/li>\n<\/ol>\n

            Show by integration that the velocity, v, of the box is given by v = 3 + 4t.<\/p>\n

             <\/p>\n

              \n
            1. The equation for the velocity, v, of a moving trolley is v = 2 + 6t.<\/li>\n<\/ol>\n

              Derive an expression for the displacement, s, of the trolley.<\/p>\n

               <\/p>\n

              9.\u00a0\u00a0 A projectile is launched from the top of a building with an initial speed of 20 m s-1<\/span><\/sup> at an angle of 30\u00b0 to the horizontal. The height of the building is 30 m.<\/p>\n

              (a)\u00a0\u00a0 Calculate how long it takes the projectile to reach the ground.<\/p>\n

              (b)\u00a0\u00a0 Calculate the velocity of the projectile on impact with the ground, (magnitude and direction).<\/p>\n","protected":false},"excerpt":{"rendered":"

              \u00a0 Equations of motion   1\u00a0\u00a0 The displacement, s in metres, of an object after a time, t in seconds, is given by s = 90t \u2013 4 t2 (a)\u00a0\u00a0 Find by differentiation the equation for its velocity. (b)\u00a0\u00a0 At what time will the velocity be zero? (c)\u00a0\u00a0 Show that the acceleration is a constant … Continue reading Tutorial 1<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":6460,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/4","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/users\/6460"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/comments?post=4"}],"version-history":[{"count":2,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/4\/revisions"}],"predecessor-version":[{"id":9,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/4\/revisions\/9"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/media?parent=4"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}