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Answer:
a) 4 s
b) 36 m/s²
c) 54 m
Explanation:
s = 2t³ – 24t + 6
a) Find t when v = 72 m/s.
v = ds/dt
v = 6t² – 24
72 = 6t² – 24
6t² = 96
t = 4
b) Find a when v = 30 m/s.
a = dv/dt
a = 12t
When v = 30:
30 = 6t² – 24
6t² = 54
t = 3
a = 36
c) Find Δs between t = 1 and t = 4
Δs = (2(4)³ – 24(4) + 6) – (2(1)³ – 24(1) + 6)
Δs = 38 – (-16)
Δs = 54
1) 1.08 m/s^2
Explanation:
Acceleration is equal to the change in velocity divided by the time taken:

where
v is the final velocity
u is the initial velocity
is the time taken
In this problem, we have:
- initial velocity: u = 0 (you start from rest)
- final velocity: v = 5.4 m/s
- time taken: 
Therefore, the acceleration is

2) -0.54 m/s^2
We can calculate the acceleration to slow down using the same formula as before, but this time the data are as follows:
- initial velocity : u = 5.4 m/s
- final velocity : v = 0 (you come to a stop)
- time taken : 
using the same formula, we find

And the negative sign means it is a deceleration.
A car is traveling due north at 23.6 m>s.
Find the velocity of the car after 7.10 s if its
acceleration is
The acceleration is known to be: a(t) = 1.7 m/s2.
We must integrate over time to obtain the velocity function, and the results are:
v(t) = (1.7m/s^2)
*t + v0
If we suppose that we begin at 23.6 m/s, then the initial velocity is: v0 = 23.6 m/s, where v0 is the beginning velocity.
The velocity formula is then: v(t) = (1.7m/s2).
*t + 23.6 m/s
We now seek to determine the value of t such that v(t) = 27.8 m/s.
Consequently, v(t) = 27.8 m/s = (1.7 m/s2)
*t + 23.6 m/s = (1.7 m/s2) 27.8 m/s - 23.6 m/s
t = 2.5 seconds when *t 4.2 m/s = (1.7 m/s/2)
At such acceleration, 2.5 seconds are required.
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Answer
given,
height of aquarium = 6 m
Depth of fresh water = D = 1.50 m
horizontal length of the aquarium(w) = 8.40 m
total force increased when liquid is filled to depth = 4.30 m
g = 9.81 m/s²
ρ = 998 Kg/m³
force in the aquarium.
dF = PdA





At D = 1.5 m

F = 9.08 x 10⁴ N
At D = 4.30 m

F = 7.46 x 10⁵ N
Total force on the wall increased by
ΔF = 74.6 x 10⁴ - 9.08 x 10⁴
ΔF = 65.52 x 10⁴ N