(25%) Vehicle Dynamics Problem: A vehicle moving on the (approximatelyflat) surface of the moon travels in a path (position vector) specified by R =((0.2t) m/s)î + ((0.3t2) m/s2)ĵ, where R is the position vector, and t is the time,in seconds. Using vector calculus, derive the vector representations for thevelocity and acceleration of the vehicle. Calculate the velocity and acceleration(both magnitude and direction) at t = 2.0 sec.4. (25%) Newtonian Mechanics Problem: A car is traveling at 90 miles per hourdown a paved, asphalt road in good condition (no potholes, speed bumps, oilslicks, etc.) starting at t = 0sec. The driver sees a sheep standing in the road 200feet away.a. The driver steps on the brake, decelerating at a constant rate (expressed inm/s^2), without skidding, to avoid hitting the sheep in the road. If the driverdoesn’t want to experience too rapid a deceleration, a constant deceleration(negative acceleration) greater than a = - 15 m/s2 (horizontally) to avoidpossible bodily injury, and is only able to decelerate in a straight line, howlong does it take the driver to stop (seconds)? Assume the car starts at x=x0 = 0.0m.b. Can a collision with the sheep be avoided in this case (Yes/No)?c. What is the minimum constant deceleration (negative acceleration)necessary to avoid hitting the sheep (m/s2)? At what time does the car stop(seconds)?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(25%) Vehicle Dynamics Problem: A vehicle moving on the (approximately
flat) surface of the moon travels in a path (position vector) specified by R =
((0.2t) m/s)î + ((0.3t2) m/s2)ĵ, where R is the position vector, and t is the time,
in seconds. Using vector calculus, derive the vector representations for the
velocity and acceleration of the vehicle. Calculate the velocity and acceleration
(both magnitude and direction) at t = 2.0 sec.
4. (25%) Newtonian Mechanics Problem: A car is traveling at 90 miles per hour
down a paved, asphalt road in good condition (no potholes, speed bumps, oil
slicks, etc.) starting at t = 0sec. The driver sees a sheep standing in the road 200
feet away.
a. The driver steps on the brake, decelerating at a constant rate (expressed in
m/s^2), without skidding, to avoid hitting the sheep in the road. If the driver
doesn’t want to experience too rapid a deceleration, a constant deceleration
(negative acceleration) greater than a = - 15 m/s2 (horizontally) to avoid
possible bodily injury, and is only able to decelerate in a straight line, how
long does it take the driver to stop (seconds)? Assume the car starts at x=
x0 = 0.0m.
b. Can a collision with the sheep be avoided in this case (Yes/No)?
c. What is the minimum constant deceleration (negative acceleration)
necessary to avoid hitting the sheep (m/s2)? At what time does the car stop
(seconds)?

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