Explanation Given: The initial speed of the car is 25 mi / h . The distance of the intersection is 65 m . The length of the car is 4.5 m . The width of the intersection is 15 m . Time before light turns red is 5.0 s . Time taken to start the acceleration is 1.0 s . Formula used: Write the expression for total distance covered by the car. x t o t a l = x 1 + x 2 + x 3 ..............(1) Here, x t o t a l is the total distance covered by the car, x 1 is the distance of the yellow light from the car, x 2 is the width of the intersection and x 3 is the length of the car. Write the expression for distance covered before started accelerating. x b = v i t ..............(2) Here, x b is the distance covered before accelerating, v i is the initial velocity of the car and t is the time before car starts accelerating. Write the expression for distance travelled when accelerating. x a = x t o t a l − x b Here, x a is the distance covered while accelerating Write expression for distance travelled with the constant acceleration. x a = v i t a + 1 2 a t a 2 ..............(3) Here, t a is the time for which car is accelerated and a is the acceleration of the car. Write the expression for final velocity of the car. v f = v i + a t a Here, v f is the final velocity of the car. Rearrange above expression for a . a = v f − v i t a Substitute v f − v i t a for a in equation (3). x a = v i t a + 1 2 ( v f − v i t a ) t a 2 x a = v i t a + 1 2 ( v f − v i ) t a x a = v i t a + 1 2 v f t a − 1 2 v i t a x a = 1 2 t a ( v i + v f ) Substitute x t o t a l − x b for x a in above expression and solve for v f

6th Edition

ISBN: 9781429206099

Author: Tipler

Publisher: MAC HIGHER

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Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –

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Chapter 2, Problem 121P

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The speed of the car as it exits the intersection.

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Chapter 2, Problem 120P

Chapter 2, Problem 122P

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