If s= (7t^2 ) m, where t is in seconds, determine v when t= 5s.

2. A particle on a damped spring has an acceleration of x = -5x -0.2x. It has an initial position of x(0) m = 2 m and an initial velocity of x (0) = 3. Find the position and velocity at t = 4 s. Assume all values are given to three significant figures. Please use any method learned in class: Trial Solution Method, Euler Method, or Laplace Transformation. Show all work.

A car travels along a path described as y = p and an when x = 2 m and x = 6 m. Round all answers to three (3) significant digits When = = 2m: P₁ = 15.8 an = 5.13 When x = 6 m: P2 = 84.4 an = 0.96 x m X m x m X m 2² ²+2 and has a constant velocity of v = 9 8 m What is the

+51 suspension You are an engineer designing the suspension of an ATV. You want to ensure that the vehicle doesn't "bottom out" even when landing from being airborne. An approximation describing the vertical acceleration of the suspension upon impact is I a(s) 9.8(1 12s) m/s² where the initial velocity at impact is v=1.5 m/s with the spring initially uncompressed, s = 0 m A) What is the vertical velocity of the ATV chassis after the spring is compressed 0.1 m? B) What is the maximum distance the spring gets compressed? (This occurs when the ATV's vertical motion comes momentarily to rest)

1. The slope of a v-t graph at any instant represents instantaneous a. Velocity b. Acceleration c. Position d. Jerk