7. The velocity m s–1 of an object after seconds is given by = , for 0 25. v t v(t) t ≤ ≤ (a) On the grid sketch the graph of clearly indicating the maximum point. v, Let be the distance travelled in the first nine seconds. d (b) (i) Write down an expression for d. (ii) Hence, write down the value of d. Answers: (x) = 4x3  2x + 3 f 2. (a) = = (m s-2) a –10 (b) = d = 50t 5t2 + 40 s ∫v – 3. (a) (b) = 16 I 4. = 9 a 5. (a) = 40t s (ii) = 40t s (b) (i) at station, so = 0 v = (seconds) t (ii) = a (c) = 10 t = 200 s since 200 < 500 train stops before the station 6. (a) area = 52.1 (b) = 6.79 a 7. (a) (b) (i) = d (ii) = 148.5 (m) d
7. The velocity v m s–1 of an object after t seconds is given by v(t) = , for 0 ≤ t ≤ 25. (a) On the grid sketch the graph of v, clearly indicating the maximum point. Let d be the distance travelled in the first nine seconds. (b) (i) Write down an expression for d. (ii) Hence, write down the value of d. Answers: f (x) = 4x3  2x + 3 2. (a) a = = –10 (m s-2) (b) s = ∫v d = 50t – 5t2 + 40 3. (a) (b) I = 16 4. a = 9 5. (a) s = 40t (ii) s = 40t (b) (i) at station, so v = 0 t = (seconds) (ii) a = (c) t = 10 s = 200 since 200 < 500 train stops before the station 6. (a) area = 52.1 (b) a = 6.79 7. (a) (b) (i) d = (ii) d = 148.5 (m)
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