Date | November 2017 | Marks available | 4 | Reference code | 17N.2.SL.TZ0.S_9 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | S_9 | Adapted from | N/A |
Question
Note: In this question, distance is in metres and time is in seconds.
A particle P moves in a straight line for five seconds. Its acceleration at time is given by , for .
When , the velocity of P is .
Write down the values of when .
Hence or otherwise, find all possible values of for which the velocity of P is decreasing.
Find an expression for the velocity of P at time .
Find the total distance travelled by P when its velocity is increasing.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A1A1 N2
[2 marks]
recognizing that is decreasing when is negative (M1)
eg, sketch of
correct interval A1 N2
eg
[2 marks]
valid approach (do not accept a definite integral) (M1)
eg
correct integration (accept missing ) (A1)(A1)(A1)
substituting , (must have ) (M1)
eg
A1 N6
[6 marks]
recognizing that increases outside the interval found in part (b) (M1)
eg, diagram
one correct substitution into distance formula (A1)
eg
one correct pair (A1)
eg3.13580 and 11.0833, 20.9906 and 35.2097
14.2191 A1 N2
[4 marks]