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Motion in Straight Line

Kinematic equations for uniformly accelerated motion

A driver travelling at 30 {kph} sees the light turn red at the

Question

Medium

Solving time: 3 mins

A driver travelling at $30 kph$ sees the light turn red at the intersection. If his reaction time is $0.6 s$ , and the car can decelerate at $4.5 m / s^{2}$ , find the stopping distance of the car. What would the stopping distance be if the car were moving at $90 kph$ .

Views: 5,764 students

Updated on: Jun 7, 2023

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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James Discussed

A driver travelling at

30 kph

sees the light turn red at the intersection. If his reaction time is

0.6 s

, and the car can decelerate at

4.5 m / s^{2}

, find the stopping distance of the car. What would the stopping distance be if the car were moving at

90 kph

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Initial speed of car is

= 30 kph = 8.3 m / s

.
Reaction time of driver is

0.6 s

, it is the duration she takes to put the brakes on and in this duration car travels with the uniform speed.
The distance travelled by the car during her reaction time is

= 8.34 \times 0.6 = 5 m

.
Now after travelling

5 m

, car start decelerating at

4.5 m / s^{2}

.
As final velocity of the car is zero, when it comes to rest, we have for its initial velocity

u = 2 a s

.
The distance travelled by the car before coming to rest can be given as

s = \frac{u ^{2}}{2 a} = \frac{( 8.34 ) ^{2}}{2 \times 4.5} = 7.71 m

Total stopping distance is

= 5 + 7.71 = 12.71 m

.
If initial speed of car were

90 kph

25 m / s

, the distance travelled by car during reaction time of driver will become

25 \times 0.6 = 15 m

and the second distance will change as

s = \frac{( 25 ) ^{2}}{2 \times 4.5} = 69.45 m

.
Total stopping distance is

= 15 + 69.45 = 84.45 m

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Question Text	A driver travelling at $30 kph$ sees the light turn red at the intersection. If his reaction time is $0.6 s$ , and the car can decelerate at $4.5 m / s^{2}$ , find the stopping distance of the car. What would the stopping distance be if the car were moving at $90 kph$ .
Updated On	Jun 7, 2023
Topic	Motion in Straight Line
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	664
Avg. Video Duration	4 min

A driver travelling at $30 kph$ sees the light turn red at the intersection. If his reaction time is $0.6 s$ , and the car can decelerate at $4.5 m / s^{2}$ , find the stopping distance of the car. What would the stopping distance be if the car were moving at $90 kph$ .

Text solutionVerified

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A driver travelling at 30kph sees the light turn red at the intersection. If his reaction time is 0.6 s, and the car can decelerate at 4.5 m/s2, find the stopping distance of the car. What would the stopping distance be if the car were moving at 90kph.

Text solutionVerified

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A driver travelling at $30 kph$ sees the light turn red at the intersection. If his reaction time is $0.6 s$ , and the car can decelerate at $4.5 m / s^{2}$ , find the stopping distance of the car. What would the stopping distance be if the car were moving at $90 kph$ .