EAS 208 Dynamics Lecture

Task in EAS 208 Dynamics Lecture

Q1-1: The acceleration of a particle is defined by a = – (0.1 + sin 0.8) m/s2 where s is the displacement. If the velocity of the particle is v = 1 m/s when s = 1 m, find

(a) the velocity at s = -1 m,
(b) the position where the velocity is maximum,
(c) the maximum velocity.

Q1-2: For the particle with v-t graph shown below, plot s-t and a-t graphs for the same time intervals. Show all the values on the plots. Note that at t = 0, s = 0.

Q1-3: A ball is thrown from a point 1 m above the ground as shown. The initial velocity is v0 and the angle to the horizon is 25°. If the ball slightly touches the fence 110 m away
and passes over it, determine

(a) the initial velocity v0,
(b) the maximum height h that the ball can reach,
(c) the time that takes the ball to reach the fence.

Q1-4: A particle leaves its initial position with the initial velocity of 5√2 ft/s. Find the angle for which the particle will hit the surface at the final position.

Q1-5: The speed of the car shown below increases at a constant rate from 50 mi/h at point A to 65 mi/h at B. Find the magnitude of the car acceleration 2 seconds after it passes point A?

Q1-6: A ball is rolling on a surface for which f(x) = 2×2 – 4x + 5. The ball passes point A (x0 = 4 m ) with the speed v = 5 m/s, which increases at the rate of 4 m/s2. Find\

(a) the normal and tangential components of the acceleration of the ball as it passes point A,

(b) the angle between the acceleration and velocity vectors. EAS 208 Dynamics Lecture