2. 1D Motion / Kinematics

A particle moving along the x-axis has its veocity described by the function v_x = 2t² m/s, where t is in s. itsinitial position is x₀ = 1 m at t₀ = 0 s. At t = 1 s, what are the particle's position?

Careful measurements have been made of Olympic sprinters in the 100 meter dash. A quite realistic model is that the sprinter's velocity is given by v_𝓍 = a ( 1 - e⁻ᵇᵗ ) where t is in s, v_𝓍 is in m/s, and the constants a and b are characteristic of the sprinter. Sprinter Carl Lewis's run at the 1987 World Championships is modeled with a = 11.81 m/s and b = 0.6887 s⁻¹. Find an expression for the distance traveled at time t.

Draw a pictorial representation for the following problem. Do not solve the problem. What acceleration does a rocket need to reach a speed of 200 m/s at a height of 1.0 km?

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?

Problems 49, 50, 51, and 52 show a partial motion diagram. For each: Draw a pictorial representation for your problem.

A bowling ball rolls up an incline and then onto a smooth, level surface. Draw a complete motion diagram of the bowling ball. Don't try to find the acceleration vector at the point where the motion changes direction; that's an issue for Chapter 4.

The position of a particle is given by the function x = (2t³ - 6t² + 12) m, where t is in s. At what time is the acceleration zero?

FIGURE EX1.10 shows two dots of a motion diagram and vector. Copy this figure, then add dot 4 and the next velocity vector if the acceleration vector at dot 3 points left.