A student integrates a velocity function and writes

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A student integrates a velocity function

v(t)

and writes

s(t)=\int v(t)\,dt + C

. Which of the following best justifies how the constant

C

is determined? (a) Choose

C=0

because adding a constant does not affect the derivative of

s(t)

. (b) Set

v(0)=0

and use that value to find

C

. (c) Evaluate

s(t)

at the time when the particle’s position is known and solve for

C

. (d) Differentiate

s(t)

twice and equate the result to

v(t)

to determine

C