2.4-2.5
Your guide: Sir HamzaBelieves every formula has a story, and units never lie.
A cricket ball is thrown up. It slows, stops, and falls. Its motion follows three short equations.
Let us learn them and when to use each.
The book gives three equations. They hold only when acceleration is constant.
v_f = vᵢ + at (Eq. 2.11).
S = vᵢt + ½at2 (Eq. 2.14).
2aS = v_f2 − vᵢ2 (Eq. 2.16).
The book derives them two ways: by algebra and by graph. The graph is a velocity-time line. The area under it is S.
List what you know. Find what is missing. Pick the equation without the missing one.
No S? Use v_f = vᵢ + at. No v_f? Use S = vᵢt + ½at2. No t? Use 2aS = v_f2 − vᵢ2.
Book Example 2.2: vᵢ = 10 m s−1, a = 2 m s−2, t = 5 s gives v_f = 20 m s−1.
Book Example 2.3 gives S = 76 m.
Book Example 2.4: change units first. 300 km/h = 83.33 m s−1. Then a = 7.72 m s−2 and S = 450 m.
A falling body has constant acceleration g = 9.8 m s−2 (the book's value).
So use the same three equations. Replace a by g, and S by h.
Going up, g is negative. Going down, it is positive.
Book Example 2.5 gives t = 3.34 s, v_f = 32.7 m s−1 and h = 54.56 m. The last uses the rounded 32.7.
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A cricket ball is thrown up. It slows, stops, and falls. Its motion follows three short equations.
Let us learn them and when to use each.
The book gives three equations. They hold only when acceleration is constant.
v_f = vᵢ + at (Eq. 2.11).
S = vᵢt + ½at2 (Eq. 2.14).
2aS = v_f2 − vᵢ2 (Eq. 2.16).
The book derives them two ways: by algebra and by graph. The graph is a velocity-time line. The area under it is S.
List what you know. Find what is missing. Pick the equation without the missing one.
No S? Use v_f = vᵢ + at. No v_f? Use S = vᵢt + ½at2. No t? Use 2aS = v_f2 − vᵢ2.
Book Example 2.2: vᵢ = 10 m s−1, a = 2 m s−2, t = 5 s gives v_f = 20 m s−1.
Book Example 2.3 gives S = 76 m.
Book Example 2.4: change units first. 300 km/h = 83.33 m s−1. Then a = 7.72 m s−2 and S = 450 m.
A falling body has constant acceleration g = 9.8 m s−2 (the book's value).
So use the same three equations. Replace a by g, and S by h.
Going up, g is negative. Going down, it is positive.
Book Example 2.5 gives t = 3.34 s, v_f = 32.7 m s−1 and h = 54.56 m. The last uses the rounded 32.7.
Q1. A body falls from rest for 2 s. Find v_f with g = 9.8.
vᵢ = 0, so v_f = 0 + 9.8 × 2 = 19.6 m s−1.
✗ “Use a = 9.8 always for gravity, even going up.”
✓ Going up, g acts against motion. Use −9.8.
✗ “Use the three equations for any motion.”
✓ Only when acceleration is constant.
1. Which equation has no t?
(c) Eq. 2.16 has a, S, v_f, vᵢ only.
2. A car starts from rest. a = 2 m s−2, t = 5 s. S is:
(a) S = ½ × 2 × 25 = 25.
3. The book's value of g is:
(a) Section 2.5 uses g = 9.8 m s−2.
4. The area under a velocity-time graph gives:
(b) The book uses this area to get S.
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