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Date November 2017 Marks available 5 Reference code 17N.1.AHL.TZ0.H_5
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Find Question number H_5 Adapted from N/A

Question

A particle moves in a straight line such that at time t seconds ( t 0 ) , its velocity v , in m s 1 , is given by v = 10 t e 2 t . Find the exact distance travelled by the particle in the first half-second.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

s = 0 1 2 10 t e 2 t d t

attempt at integration by parts     M1

= [ 5 t e 2 t ] 0 1 2 0 1 2 5 e 2 t d t     A1

= [ 5 t e 2 t 5 2 e 2 t ] 0 1 2     (A1)

 

Note:     Condone absence of limits (or incorrect limits) and missing factor of 10 up to this point.

 

s = 0 1 2 10 t e 2 t d t     (M1)

= 5 e 1 + 5 2   ( = 5 e + 5 2 )   ( = 5 e 10 2 e )     A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5 —Calculus » SL 5.9—Kinematics problems
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Topic 5 —Calculus

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