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AQA GCSE · Question 03.5 · Space physics
The distance between Arcturus and the Earth is 3.6 × 10¹⁴ km.
speed of light = 3.0 × 10⁸ m/s
Calculate the time taken for light from Arcturus to reach the Earth. Use the Physics Equations Sheet.
The distance between Arcturus and the Earth is 3.6 × 10¹⁴ km.
speed of light = 3.0 × 10⁸ m/s
Calculate the time taken for light from Arcturus to reach the Earth. Use the Physics Equations Sheet.
How to approach this question
1. Identify the equation linking speed, distance, and time.
2. Check the units. The distance is in km, but the speed is in m/s. You must convert the distance to metres.
3. Rearrange the equation to make time the subject.
4. Substitute the values and calculate the result. Remember the rules for dividing numbers in standard form.
Full Answer
1. Convert distance to metres:
d = 3.6 × 10¹⁴ km = 3.6 × 10¹⁴ × 1000 m = 3.6 × 10¹⁷ m
2. Equation: speed = distance / time => time = distance / speed
3. Substitute: time = (3.6 × 10¹⁷ m) / (3.0 × 10⁸ m/s)
4. Calculate: time = 1.2 × 10⁹ s
To solve this problem, we use the equation relating speed, distance, and time:
speed (v) = distance (s) / time (t)
We need to find the time, so we rearrange the equation:
t = s / v
First, we must ensure the units are consistent. The speed is in m/s, so the distance must be in metres.
Given distance s = 3.6 × 10¹⁴ km.
To convert km to m, we multiply by 1000 (or 10³):
s = 3.6 × 10¹⁴ × 10³ m = 3.6 × 10¹⁷ m
Now substitute the values into the rearranged equation:
t = (3.6 × 10¹⁷ m) / (3.0 × 10⁸ m/s)
To divide numbers in standard form, we divide the numbers and subtract the powers:
t = (3.6 / 3.0) × 10⁽¹⁷⁻⁸⁾ s
t = 1.2 × 10⁹ s
Common mistakes
✗ Forgetting to convert the distance from km to m. This is the most common error.\n✗ Rearranging the equation incorrectly.\n✗ Making errors when dividing numbers in standard form (e.g., adding or multiplying the indices instead of subtracting).
Practice the full AQA GCSE Physics Higher Tier Paper 2
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