Applications of Integration
For an object in motion along a line with acceleration described by , how many times between t=0 and t=10 do velocity and acceleration have opposite signs?
Four times
Three times
Once
Twice
If the velocity function of an object is given by , what is the expression for the acceleration function ?
If the position function of a car is given by , what is the velocity of the car at ?
26
33
11
18
If the velocity function of a ball is , what is the acceleration of the ball at ?
24
22
28
14
Given a particle's position function on a coordinate plane as , how would you find its speed at time t?
Integrate the function from time zero to time t.
Find , which represents acceleration, then take its absolute value.
Calculate for any value of t.
Substitute t into , then divide by t.
If displacement from origin after a certain duration is represented through , then during which intervals is the object's instantaneous speed decreasing?
When T ∈ (-∞, 0] U [1, ∞)
When T < 0
When T > 1
When T ∈ (-∞, -1) U (0, ∞)
Consider a particle moving along a path. The acceleration function of the particle is given by . What is the velocity function of the particle?
v(t) = 6
v(t) = 3t^2 + t + C
v(t) = 3t^2 + 2t + C
v(t) = 6t + C

How are we doing?
Give us your feedback and let us know how we can improve
Which graph would represent an object at rest based on its position-time graph ?
A sloping line moving upwards
A wavy line oscillating above and below the t-axis
A parabolic curve opening upwards
A horizontal line
Consider a particle moving along a path. The position function of the particle is given by . What is the velocity function of the particle?
Given that a particle's velocity function is defined as , at which value of t does the acceleration function take on its maximum value?