Calculus AB Position Velocity Acceleration

A particle moves in a straight line with a velocity of v(t) = 2t². How far does the particle move between times t = 1 and t = 3?

• 18

• 52/3

• 26/3

• 16

For times t > 0, a particle moves on the x axis with its acceleration defined by a(t) = 6t – 2. If the velocity of the particle is -7 at t = 1, then at what time is the particle at rest?

• t = 4

• t = 1

• t = 2

• t = 4/3

A particle moves along the x axis with its acceleration given by a(t) = t² – 2t for 0 < t < 6. At time t = 0, the velocity is 10. What is the maximum velocity of this particle on the specified interval?

• 10

• 26

• 40

• 46

A body moves along the x-axis with its acceleration at any time t, given by a(t) = 2t – 1. If the velocity of the body at t = 0 is -6, what is the total distance traveled during the time interval 0 < t < 5?

• 5/6

• 21 5/6

• 26 1/6

• 15 1/6

A particle moves along the x-axis with velocity given by v(t) = 3t² + 6t for time t > 0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at t = 1?

• 4

• 6

• 9

• 11

Describe the speed of the object from 4-6 seconds using the distance vs. time graph.

• Increasing speed
• Decreasing speed
• Not moving
• Constant speed

According to the graph how far does the person travel in the first 5 seconds?

• 2 m
• 10 m
• 0 m
• 5 m

Given the position function, find the velocity at t=7

• 10
• 6
• 11
• 1

Given the position function, find the position at t=5

• -320
• 275
• -180
• -100

Given the position function, find the acceleration at t=8

• -2
• 1
• 2
• 3