1 Convert 90 kilometres per hour to (a) miles per hour (b) meters per second
?.
2 The driver of a car steps on the brakes, and the velocity drops from 
due east to 
due east in a time of 2 seconds. What is the acceleration?
Er. due vie ii.
The correct answer and explanation is:
Question 1: Convert 90 kilometers per hour to:
(a) miles per hour (b) meters per second
Solution:
- Convert to miles per hour (mph):
- Conversion factor: 1 km=0.621371 miles1 \, \text{km} = 0.621371 \, \text{miles}
- 90 km/h×0.621371=55.92339 mph90 \, \text{km/h} \times 0.621371 = 55.92339 \, \text{mph}
- Answer: 90 km/h=55.92 mph90 \, \text{km/h} = 55.92 \, \text{mph} (rounded to 2 decimal places)
- Convert to meters per second (m/s):
- Conversion factor: 1 km/h=10003600=0.277778 m/s1 \, \text{km/h} = \frac{1000}{3600} = 0.277778 \, \text{m/s}
- 90 km/h×0.277778=25 m/s90 \, \text{km/h} \times 0.277778 = 25 \, \text{m/s}
- Answer: 90 km/h=25 m/s90 \, \text{km/h} = 25 \, \text{m/s}
Question 2: Determine the acceleration of the car.
Given:
- Initial velocity (uu) = 25 m/s25 \, \text{m/s} (assumed from the question context)
- Final velocity (vv) = 0 m/s0 \, \text{m/s} (as the car stops)
- Time (tt) = 2 s2 \, \text{s}
Formula for acceleration (aa):
a=v−uta = \frac{v – u}{t}
Calculation:
a=0−252=−12.5 m/s2a = \frac{0 – 25}{2} = -12.5 \, \text{m/s}^2
- The negative sign indicates deceleration.
- Answer: The acceleration is −12.5 m/s2-12.5 \, \text{m/s}^2.
Explanations (300 words):
- Question 1 Explanation: To convert speeds between units, you use standard conversion factors. 1 km1 \, \text{km} equals 0.621371 miles0.621371 \, \text{miles}, so multiplying 90 km/h90 \, \text{km/h} by 0.6213710.621371 converts it to miles per hour. Similarly, converting to meters per second requires dividing kilometers by the number of seconds in an hour. Thus, 90 km/h=25 m/s90 \, \text{km/h} = 25 \, \text{m/s}. This is useful for comparing speeds in different unit systems.
- Question 2 Explanation: Acceleration measures the rate of change of velocity over time. If a car’s velocity decreases, the acceleration is negative, termed deceleration. The formula for acceleration is a=v−uta = \frac{v – u}{t}, where vv is final velocity, uu is initial velocity, and tt is the time taken. Substituting the given values (u=25 m/s,v=0 m/s,t=2 su = 25 \, \text{m/s}, v = 0 \, \text{m/s}, t = 2 \, \text{s}), the acceleration is −12.5 m/s2-12.5 \, \text{m/s}^2. This means the car slows down at a rate of 12.5 m/s212.5 \, \text{m/s}^2 every second.