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  1. AP Calculus
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Applications of Integration

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

For an object in motion along a line with acceleration described by a(t)=sin⁡(πt)a(t)=\sin(\pi t)a(t)=sin(πt), how many times between t=0 and t=10 do velocity and acceleration have opposite signs?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

If the velocity function v(t)v(t)v(t) of an object is given by v(t)=3t2−2t+1v(t) = 3t^2 - 2t + 1v(t)=3t2−2t+1, what is the expression for the acceleration function a(t)a(t)a(t)?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

If the position function of a car is given by s(t)=3t3−2t2+5ts(t) = 3t^3 - 2t^2 + 5ts(t)=3t3−2t2+5t, what is the velocity of the car at t=2t = 2t=2?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If the velocity function of a ball is v(t)=5t2+2tv(t) = 5t^2 + 2tv(t)=5t2+2t, what is the acceleration of the ball at t=2t = 2t=2?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

Given a particle's position function on a coordinate plane as s(t)=t3−92t2s(t) = t^3 - \frac{9}{2}t^2s(t)=t3−29​t2, how would you find its speed at time t?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

If displacement from origin after a certain duration is represented through S(T)=T3T2+1S(T)=\frac{T^3}{T^2+1}S(T)=T2+1T3​, then during which intervals is the object's instantaneous speed decreasing?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Consider a particle moving along a path. The acceleration function of the particle is given by a(t)=6t+2a(t) = 6t + 2a(t)=6t+2. What is the velocity function of the particle?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

Which graph would represent an object at rest based on its position-time graph s(t)s(t)s(t)?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

Consider a particle moving along a path. The position function of the particle is given by s(t)=t3−2t2+4t−3s(t) = t^3 - 2t^2 + 4t - 3s(t)=t3−2t2+4t−3. What is the velocity function of the particle?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

Given that a particle's velocity function is defined as v(t)=t4−4t3v(t) = t^4 - 4t^3v(t)=t4−4t3, at which value of t does the acceleration function take on its maximum value?