// Numbas version: finer_feedback_settings {"name": "Q2 Constant Acceleration", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Q1.png", "/srv/numbas/media/question-resources/Q1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["s", "u", "a", "t", "s1", "v1", "t1", "s2", "t2"], "name": "Q2 Constant Acceleration", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

(a)	\n $u = \\var{u}; a = \\var{a}; t = \\var{t}; s = \\,?$ \n

	\n Using $s = ut+\\frac{1}{2}at^{2}$ gives \n

	\n $s = (\\var{u} \\times \\var{t})+(\\frac{1}{2}\\times\\var{a}\\times(\\var{t})^{2}) = \\var{precround(s1,3)}\\,$ metres \n
	\n \n
(b)	\n Find the speed of the sprinter after $\\var{t}$ seconds using $v = u + at$ \n

	$v = \\var{u}+(\\var{a}\\times\\var{t}) = \\var{precround(v1,3)}\\,ms^{-1}$
	\n \n
(c)	\n After the first $\\var{t}$ seconds, the sprinter runs the remainder of the race $(\\var{s}-\\var{precround(s1,3)})\\,$ metres at a constant speed of $\\var{precround(v1,3)}\\,ms^{-1}$ \n

	\n So the time to run the remainder of the race is $\\frac{\\var{s}-\\var{precround(s1,3)}}{\\var{precround(v1,3)}} = \\var{precround(t2,3)}\\,$ seconds \n

	\n Total time for the $\\var{s}\\,$ metre race is then $\\var{precround(t2,3)}+\\var{t} = \\var{precround(t1,3)}\\,$ seconds \n

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The distance travelled by the sprinter in the first $\\var{t}\\,$ seconds = [[0]] metres

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The speed of the sprinter at the end of $\\var{t}\\,$ seconds = [[0]] $ms^{-1}$

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The total time for the race = [[0]] seconds

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A sprinter emerges from the blocks with an initial speed of $\\var{u}\\,ms^{-1}$ and accelerates uniformly at $\\var{a}\\,ms^{-2}$ for the first $\\var{t}\\,$ seconds of a $\\var{s}\\,$ metre race

The sprinter then maintains a constant speed to the end of the race

Assuming the sprinter moves in a straight line

(a) Find the distance travelled by the sprinter in the first $\\var{t}\\,$ seconds

(b) Find the speed of the sprinter at the end of the first $\\var{t}\\,$ seconds

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