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: 9781429281843

Author: Tipler

Publisher: MAC HIGHER

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Distance and Speed

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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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