Find the Acceleration Given a Position Function| University Physics

An object moves along the x-axis. The position as a function of time is given by c(t)=at^3+bt+c. What is the object's acceleration at time t = 0.50 s?

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Rank the diagrams according to the x-component of the acceleration| University Physics

The figure below shows six different motion diagrams. The separation between dots is in the same scale in all diagrams, and the time interval between dots is also the same for all of them. The direction of the positive x-axis is also shown. Rank the diagrams according to the x-component of the acceleration. (Positive is greater than negative)

Starship Enterprise and Klingon Ship Problem on Physics| University Physics

The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 51 km/s. To the crew's great surprise, a Klingon ship is 150 km directly ahead, traveling in the same direction at a mere 21 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just about 5.0 s. The Enterprise's computers react instantly to brake the ship. PART A. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant.