What is the distance a ball falls after 1,2,3,4,5 seconds (assumeg is rounded to 10
m/?)?
A) 10, 20, 30, 40, 50 m
B) 5, 20, 45, 80,125 m
C) 5, 10,15, 20, 25 m
D) 10, 25, 60, 90,120 m
Answers
Answer:
Let’s review the 4 fundamental kinematic equations of motion for constant acceleration (strongly recommend you commit these to memory – they will serve you well):
s = ut + ½at^2 …. (1)
v^2 = u^2 + 2as …. (2)
v = u + at …. (3)
s = (u + v)t/2 …. (4)
where s is distance, u is initial velocity, v is final velocity, a is acceleration and t is time.
In this case, we know u = 0 (assumed), g = 10m/s^2 (given) and we want to know s at several values of t, so we use equation (1):
s = ut + ½at^2s1 = 0 + 5(1^1) = 5m
s2 = 0 + 5(2^2) = 20m
s3 = 0 + 5(3^2) = 45m
s4 = 0 + 5(4^2) = 80m
s5 = 0 + 5(5^2) = 125m
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Answer:
The distance a ball falls after 1, 2, 3, 4, 5 seconds is B) 5, 20, 45, 80,125 m.
Explanation:
Given:
t₁ = 1s, t₂ = 2s, t₃ = 3s, t₄ = 4s, t₅ = 5s
a = g = 10m/s²
To find:
Distances s₁, s₂, s₃, s₄, and s₅
Formula:
s = ut + (1/2)at²
Solution:
From the equations of motion, we have
s = ut + (1/2)at²
Assuming that u = 0, we get
s = 0 + (1/2)at²
s = (1/2)at²
For t₁ = 1s,
s = (1/2)(10)(1²)
s = (1/2)(10)
s = 5m
For t₂ = 2s,
s = (1/2)(10)(2²)
s = (5)(4)
s = 20m
For t₃ = 3s,
s = (1/2)(10)(3²)
s = (5)(9)
s = 45m
For t₄ = 4s,
s = (1/2)(10)(4²)
s = (5)(16)
s = 80m
For t₅ = 5s,
s = (1/2)(10)(5²)
s = (5)(25)
s = 125m
Therefore, the distances are 5m, 20m, 45m, 80m, and 125m.
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