Kinematics with Calculus

Motion sensors recorded the following data about a runner during a cross-country race. During which segment of the race did the runner have the greatest speed?

• W
• X
• Y
• Z

What is the acceleration of an object moving at constant velocity?

• 2 m/s²

• 1 m/s²

• 0 m/s²

• 0.8 m/s²

The graph shows the position of a truck vs. time. According to the graph, the velocity of the truck is...

• increasing

• remaining constant

• decreasing

The position of an object is given by the equation x = 3.0 t^2 + 1.5 t + 4.5, where x is in meters and t is in seconds. What is the instantaneous acceleration of the object at t = 3.0 s?

• 3.0 m/s/s

• 6.0 m/s/s

• 9.0 m/s/s

• 19.5 m/s/s

• 36 m/s/s

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) -2t - 1 
• v(t) = t³
• v(t) = -t

The acceleration function is the first derivative of...

• position
• velocity
• calculus
• particle motion

The position function x(t)=7t²-18t-7 is given. What is the velocity function?

• v(t)=14t-18
• v(t)=14t+18
• v(t)=18t-14
• v(t)=18t+14
  

The velocity of an object is given as v = 2t + 3t³. What is the acceleration of the object at t = 2 secs?

• 38 m/s/s
• 27 m/s/s
• 16 m/s/s
• 49 m/s/s

Given x(t)=t³-4t²+7, what is the initial position?

• 11
• -10
• 7
• 0