Dynamics HW

ENGR 2120: Dynamics

Homework #2

Assigned: 01/27/16

Due: 02/03/16

Assignment Motivation

The goal of this assignment is for students to gain a fundamental understanding of general curvilinear

motion and rectangular components.

Assignment

1. Traveling with an initial speed of 70 km/h, a car accelerates at 6000 km/h2 along a straight road. How long will it take to reach a speed of 120 km/h? Also, through what distance does the car travel during

this time?

2. The path of a particle is defined by 𝑦2 = 4𝑘𝑥, and the component of velocity along the 𝑦 axis is 𝑣𝑦 = 𝑐𝑡, where both 𝑘 and 𝑐 are constants. Determine the 𝑥 and 𝑦 components of acceleration in

terms of 𝑐, 𝑡, 𝑥, and 𝑘. 3. A particle is traveling along the parabolic path 𝑦 = 0.25𝑥2. If 𝑥 = 8 m, 𝑣𝑥 = 8 m/s, and 𝑎𝑥 = 4 m/s

2

when 𝑡 = 2 s, determine the magnitude of the particle’s velocity and acceleration at this instant.

4. A particle travels along the curve from A to B in 2 s. It takes 4 s for it to go from B to C and then 3 s

to go from C to D. Determine its average speed when it does from A to D.

5. A rocket is fired from rest at 𝑥 = 0 and travels along a parabolic trajectory described by

𝑦2 = [120(103)𝑥] m. If the 𝑥 component of acceleration is 𝑎𝑥 = ( 1

4 𝑡2) m/s2, where t is in seconds,

determine the magnitude of the rocket’s velocity and acceleration when 𝑡 = 10 s.