Question

An automobile antilock brake system (ABS) operates the brakes at 30 pulses per second. How many times do the brakes pulse in \(1.00 \mathrm{ds} ?\)

Short answer

The brakes pulse 3 times in 1 decisecond.

Step-by-step solution

Understand the Problem

We need to find out how many brake pulses occur in a time span of 1 decisecond \((1.00 \mathrm{ds})\). We are given that the ABS system operates the brakes at the rate of 30 pulses per second (1 second = 1 s).

Convert Time Units

Recognize that 1 decisecond \((1.00 \mathrm{ds})\) is equal to 0.1 seconds \((1 \mathrm{ds} = 0.1 \, \mathrm{s})\). This is important to equate the given pulse rate from seconds to deciseconds.

Calculate the Number of Pulses in 1 Decisecond

Given the rate of 30 pulses per 1 second, calculate the equivalent for 0.1 seconds. Use the formula: \[ \text{Pulses in } 1.00 \, \mathrm{ds} = 30 \, \text{pulses/second} \times 0.1 \, \mathrm{s} = 3 \, \text{pulses} \]

Interpret the Result

The calculation shows that the ABS system pulses the brakes 3 times in a span of 1 decisecond.

Key concepts

Antilock Brake System

An Antilock Brake System (ABS) is a crucial safety feature in modern automobiles designed to prevent wheel lock-up during braking. When a driver brakes sharply, the wheels can potentially stop rotating while the car is still in motion, leading to a loss of steering control. ABS tackles this by modulating the brake pressure — each wheel is individually monitored and controlled to maintain traction.

By operating at a rapid pace, ABS can apply and release the brakes multiple times per second, allowing the wheels to maintain rolling contact with the road surface. This not only helps prevent skidding but also ensures that the vehicle can still be steered while braking hard, which is vital for avoiding accidents in emergency situations.

• Maintains car steerability during braking.
• Prevents wheel lock-up and skidding.
• Enhances overall vehicle control and safety.

Overall, ABS contributes significantly to safer driving conditions, especially on slippery or uneven roads.

Pulses Per Second

Pulses per second (pps) is a measure of frequency that indicates how often a system, such as an ABS, performs a certain action within one second. In the context of an ABS, pulses per second represent how many times the brakes are modulated each second.

For example, an ABS that operates at 30 pulses per second applies and releases the brake pressure 30 times within just one second.

• This rapid pulsing allows for a more controlled deceleration of the vehicle.
• Each pulse is an application and release cycle to maintain wheel traction.
• A higher number of pulses per second usually implies better performance and safety in the braking system.

Thus, understanding the pulsating frequency gives insights into how effective an ABS is at preventing wheel lock-up and ensuring driver control.

Time Calculation

Time calculation is an essential skill, especially when converting between different units of time like seconds and deciseconds. To accurately compute how an ABS works in different units of time, it’s vital to understand these conversions.

Deciseconds (ds) are a tenth of a second. Hence, 1 decisecond equals 0.1 seconds. This conversion is crucial when calculating actions like brake pulses that occur within fractions of a second.

• To convert seconds to deciseconds, multiply by 10.
• To convert deciseconds to seconds, divide by 10.
• Example: If an ABS pulses 30 times in 1 second, it will pulse 3 times in 0.1 seconds (1 decisecond).

Mastering these time conversions allows you to determine how fractional times relate to full seconds, enhancing your problem-solving skills in physics and engineering tasks.