Explanation Given information: The speed of the car ( v C ) and truck ( v T ) is 35 mi/h . The distance ( x ) between the car and truck is 40 ft . The maximum acceleration ( a max ) of the car is 5 ft/s 2 . The maximum deceleration ( − a max ) of the car is 20 ft/s 2 . The length of the car ( x C ) is 16 ft . The length of the truck ( x T ) is 50 ft . Calculation: Tabulate the velocity ( v ) corresponding to time ( t ) as in Table (1): t (s) v ( ft/s ) 0 35 t 1 ( Δ v m ) t 2 35 Plot the v-t curve of the car with area as in Figure (1). Calculate the distance ( Δ x ) of car relative to the truck using the relation. Δ x = x C + x + x T + x Substitute 16 ft for x C , 40 ft for x and 50 ft for x T . Δ x = 16 + 40 + 50 + 40 = 146 ft Write the expression for allowable increase in speed ( Δ v m ) : Δ v m = 5 t 1 = 20 t 2 t 2 = 5 20 t 1 t 2 = 1 4 t 1 (1) Calculate the area ( A 1 ) using the relation: A 1 = 1 2 [ Δ v m t 1 ] Substitute 4.4 sec for t 1 and 5 t 1 for Δ v m . A 1 = 1 2 [ 5 t 1 2 ] Calculate the area ( A 2 ) using the relation: A 2 = 1 2 [ Δ v m t 2 ] Substitute 1 4 t 1 for t 2 and 5 t 1 for Δ v m . A 2 = 1 2 [ 5 t 1 × 1 4 t 1 ] Calculate the time ( t 2 ) using the relation: Δ x = A 1 + A 2 Substitute 146 ft for Δ x , 1 2 [ 5 t 1 2 ] for A 1 and 1 2 [ 5 t 1 × 1 4 t 1 ] for A 2

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 11.3, Problem 11.73P

To determine

The shortest time (tB) in which the driver of the car can complete the passing operation and calculate the maximum speed (vm) reached by the car and draw the v-t curve.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 11.72P

Chapter 11.3, Problem 11.74P

Students have asked these similar questions

This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A motorist starts from rest at Point A on a circular entrance ramp when t = 0, increases the speed of her automobile at a constant rate and enters the highway at Point B. Her speed continues to increase at the same rate until it reaches 85 km/h at Point C. Determine the speed at Point B. (You must provide an answer before moving on to the next part.) The speed at Point B is km/h. Note: please show step by step solution. Hence, double check the solution. For correction purposes!. I require handwritten working out please!. Kindly, please meticulously, check the image for conceptual understanding and for extra information purposes!. Also on occasions, I receive wrong answers!!. Please go through the question and working out step by step when you finish them. Appreciate your time!.

two automobiles A and B are approaching each other in adjacent highway lanes. at t=0, A and B are 3200ft apart. Their speeds are Va= 65 mi/h and Vb= 40 mi/h, and they are at points P and Q, respectively. knowing that A passes point Q 40s after B was there and that B passes point P 42s after A was there: A) determine the speed of B at the moment that it passes A in ft/s B.) when the vehicles pass each other in seconds C.) uniform acceleration of B in ft/s^2

A train which is traveling at 75 mi/hr applies its brakes as it reaches point A and slows down with a constant deceleration. Its decreased velocity is observed to be 55 mi/hr as it passes a point 1/2 mi beyond A. A car moving at 50 mi/hr passes point B at the same instant that the train reaches point A. In an unwise effort to beat the train to the crossing, the driver "steps on the gas." Calculate the constant acceleration a that the car must have in order to beat the train to the crossing by 3.3 sec and find the velocity v of the car as it reaches the crossing. Tw Answers: a = i V = i Train 75 mi/hr 1.0 mi 1.1 mil B Car 50 mi/hr ft/sec² mi/hr

Chapter 11 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

Ch. 11.1 - A bus travels the 100 miles between A and B at 50...Ch. 11.1 - Two cars A and B race each other down a straight...Ch. 11.1 - A snowboarder starts from rest at the top of a...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - The vertical motion of mass A is defined by the...Ch. 11.1 - A loaded railroad car is rolling at a constant...Ch. 11.1 - A group of hikers uses a GPS while doing a 40-mile...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - A girl operates a radio-controlled model car in a...Ch. 11.1 - The motion of a particle is defined by the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The shortest time ( t B ) in which the driver of the car can complete the passing operation and calculate the maximum speed ( v m ) reached by the car and draw the v-t curve.

Solution Summary: The author calculates the shortest time in which the driver of the car can complete the passing operation and calculate the maximum speed (t_m)

Concept explainers

Videos

The shortest time (tB) in which the driver of the car can complete the passing operation and calculate the maximum speed (vm) reached by the car and draw the v-t curve.

Want to see the full answer?

Chapter 11 Solutions