Chapter 12, Problem 13FP

1- A particle moves along the x axis. Its position varies with time according to the expression x=-41+ 2f where x is in meters and t is in seconds. The position-time graph for this motion is shown in Figure. Note that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment 1 = 1 s, and moves in the positive x direction at times /> 1 s. (A) Determine the displacement of the particle in the time intervals t=0 to 1=1 s and t= 1 s to / = 3 s. B) Calculate the average velocity during these two-time intervals C) determine the instantaneous velocity and instantaneous speed at t= 0.5 s. x(m) Slope = 4 m/s 10 00 8 9 10 O Slope =-2 m/s 1 2 015 t(s)

TACTICS BOX 1.2: Finding the acceleration vector. To find the acceleration as the velocity changes from ₁ to vƒ : (Figure 1) 27 1. Draw the velocity vectors V₁ and vf and with their tails together. 2 V 2. Draw the vector from the tip of V; to the tip of Vf. This is A because of = vi + Av. 3. Return to the original motion diagram. Draw a vector at the middle dot in the direction of Av; label it a. This is the average acceleration at the midpoint between ₁ and Vf. Vf 15

A body is moving along a straight line. Let s(t) represent the dis- placement of the body at timet from a fixed point O on the line while v(t) and a(t) represent velocity and acceleration of the body at time t respectively. 9, find v when s = 20m given that initially v = 0 and s = 10m. 40 If a = dv dv ds dev leads to the differential equation Hint: Using the fact that a for v(s): dt ds dt dv 40 V- ds s2

A particle's position is given by s = (2.17 + 4.80t2 0.100t*)m where t is in seconds and s is in meters. Find - – the particles position and acceleration at the instant when the particle has zero velocity. You may use mode + equation in your calculator to find the roots.

2/18 The graph shows the displacement-time history for the rectilinear motion of a particle during an 8-second interval. Determine the average velocity vay during the interval and, to within reasonable limits of ac- curacy, find the instantaneous velocity u when t = 4 s. s, m 10 8 6 2 0 0 2 4 t, s 6 8

A car starts form rest and reaches a speed of 48 ft per sec in 15 sec. The acceleration increases from zero uniformly with time for the first 6 sec after which it remains constant. compute the distance traveled in 15 sec

The cart shown has the following velocity as a function of time. a. What is the acceleration at 50 s, 150 s? b. If the cart started at positions = 0, sketch the displacement over time. Label the greatest displacement and state what value it is and at which time it occurs. v (m/s) 100 200 1 (s)

Q6: A particle moves along x-axis in such a way that its x coordinate varies with time t according to the equation x = (8 – 4t + 6t²) meter. Choose the diagram that represents variation of the velocity to the time.

Dynamics of rigid bodies.