calculus

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A particle moves in a straight line with velocity given by v(t) =sin t metres per second. Find the total distance travelled by the particle in the first 4 seconds of motion

• calculus -

integratiing we get

s(t) = -cost + c , where s(t) is distance and c is a constant
s(0( = -cos0 + c = -1+c
s(4) = -cos 4 + c

distance covered = -cos 4 + c - (-1+ c)
= -cos 4 + 1
= appr. 1.6536

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