The Nature of Sound?
2 answers:
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Answer:
a)
Explanation:
- Since the car speeds up at a constant rate, we can use the kinematic equation for distance (assuming that the initial position is x=0, and choosing t₀ =0), as follows:
- Since the car starts from rest, v₀ =0.
- We know the value of t = 5 sec., but we need to find the value of a.
- Applying the definition of acceleration, as the rate of change of velocity with respect to time, and remembering that v₀ = 0 and t₀ =0, we can solve for a, as follows:
- Replacing a and t in (1):
- Now, if the truck slows down at a constant rate also, we can use (1) again, noting that v₀ is not equal to zero anymore.
- Since we have the values of vf (it's zero because the truck stops), v₀, and t, we can find the new value of a, as follows:
- Replacing v₀, at and t in (1), we have:
- Therefore, as the truck travels twice as far as the car, the right answer is a).
Answer:
The acceleration of rocket B is -22.24 m/s²
Explanation:
Two rockets are flying in the same direction and are side by side at the
instant their retrorockets fire
That means they started from the same point at the same time
Rocket A has an initial velocity of 5800 m/s
Rocket B has an initial velocity of 8600 m/s
After a time t both rockets are again side by side, the displacement of
each being zero
That means they are in the same position again → s = 0
The acceleration of rocket A is -15 m/s²
We need to find the acceleration for rocket B
We can find the time from the information of rocket A by using the
rule → s = u t + a t²
where s is the displacement, u is the initial velocity, a is the
acceleration, and t is the time
→ s = 0 , u = 5800 m/s , a = -15 m/s²
Substitute these values in the rule
→ 0 = 5800 t + (-15) t²
→ 0 = 5800 t - 7.5 t²
Add 7.5 t² for both sides
→ 7.5 t² = 5800 t
Divide both sides by 7.5 t
→ t = 773.3 s
The time for the both rocket to have displacement zero is 773.3 s
Now we can find the acceleration of the rocket B by using the same
rule above
→ u = 8600 m/s , t = 773.3 , s = 0
→ 0 = (8600)(773.3) + a (773.3)²
→ 0 = 6650380 + 298996.445 a
Subtract 6650380 from both sides
→ -6650380 = 298996.445 a
Divide both sides by 298996.445
→ a = -22.24 m/s²
<em>The acceleration of rocket B is -22.24 m/s²</em>