Chapter 2: Q87P (page 38)

When the legal speed limit for New York thruway was increased from $55 mi / h$ to $65 mi / h$ , how much time was saved by a motorist who drove the 700 km between the buffalo entrance and the New York city exit at the legal speed limit?

Short Answer

Expert verified

The time saved by the motorist who drove the700 km between the Buffalo entrance and the New York City exit at the legal speed limit is 1h 13 min

Step by step solution

Given information

Distance between the buffalo entrance and the New York city $x = 700 km$

v_{1} = 55 \frac{mi}{h} v_{2} = 65 \frac{mi}{h}

To understand the concept. Relation between speed, distance and time at constant acceleration

This problem involves simple physical quantities speed, distance, and acceleration. When acceleration is constant one can say that speed is the ratio of distance and time.

Formula:

The velocity is given by,

$Δv = \frac{x}{Δt}$

Calculations for time saved by a motorist

$v_{1} = 55 \frac{mi}{hr} = 55 \frac{mi}{hr} \times (\frac{1609 m}{1 mi}) \times (\frac{1 hr}{3600 \sec}) = 24.58 m / s$

$v_{2} = 65 \frac{mi}{h} = 65 \frac{mi}{hr} \times (\frac{1609 m}{1 mi}) \times (\frac{1 hr}{3600 \sec}) = 29.05 m / s$

By the definition of velocity

$Δv = \frac{x}{Δt} Δt = \frac{x}{Δv}$

The time saved by the motorist who drove the 700 km between the Buffalo entrance and the New York City exit at the legal speed limit is

$Δt = t_{1} - t_{2} Δt = \frac{x}{v_{1}} - \frac{x}{v_{2}} Δt = \frac{700 \times 10^{3} m}{24.58 m / s} - \frac{700 \times 10^{3} m}{29.05 m / s} Δt = 4383 s = 73 \min = 1 h 13 \min = 1.2 hr$

So, the time saved by the motorist is $1.2 hr$

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When the legal speed limit for New York thruway was increased from $55 mi / h$ to $65 mi / h$ , how much time was saved by a motorist who drove the 700 km between the buffalo entrance and the New York city exit at the legal speed limit?

Short Answer

Step by step solution

Given information

To understand the concept. Relation between speed, distance and time at constant acceleration

Calculations for time saved by a motorist

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

When the legal speed limit for New York thruway was increased from 55mi/hto65mi/h, how much time was saved by a motorist who drove the 700 km between the buffalo entrance and the New York city exit at the legal speed limit?

Short Answer

Step by step solution

Given information

To understand the concept. Relation between speed, distance and time at constant acceleration

Calculations for time saved by a motorist

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Scientific Method Physics

Further Mechanics and Thermal Physics

Linear Momentum

Translational Dynamics

Force

Study anywhere. Anytime. Across all devices.

When the legal speed limit for New York thruway was increased from $55 mi / h$ to $65 mi / h$ , how much time was saved by a motorist who drove the 700 km between the buffalo entrance and the New York city exit at the legal speed limit?