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AP Calculus AB/Unit 8: Applications of Integration
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Position Function From Acceleration

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A particle moves along the xx-axis such that for any time t≥0t \geq 0, its acceleration is given by a(t)=4t3−6ta(t) = 4t^3 - 6t. If the velocity of the particle at time t=0t=0 is v(0)=1v(0) = 1 and its position at time t=0t=0 is x(0)=−1x(0) = -1, then the position of the particle at time tt is x(t)=x(t) =

A

15t5−t3+t−1\frac{1}{5}t^5 - t^3 + t - 1

B

45t5−3t3+t−1\frac{4}{5}t^5 - 3t^3 + t - 1

C

15t5−t3+t+1\frac{1}{5}t^5 - t^3 + t + 1

D

t4−3t2+t−1t^4 - 3t^2 + t - 1

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