You plug your 1 into all spots where the variable is T. Then after you’ve done this, you simply simplify the problem. Then after simplifying you should have an equation where you are simply adding and subtracting which will give you the final answer of 2.
X=3T^2-12T+5
X=3(1)^2-12(1)+5
X=(3)^2-12+5
X=9-12+5
X=2
Answer:
7.74m/s
Explanation:
Mass = 35.9g = 0.0359kg
A = 39.5cm = 0.395m
K = 18.4N/m
At equilibrium position, there's total conservation of energy.
Total energy = kinetic energy + potential energy
Total Energy = K.E + P.E
½KA² = ½mv² + ½kx²
½KA² = ½(mv² + kx²)
KA² = mv² + kx²
Collect like terms
KA² - Kx² = mv²
K(A² - x²) = mv²
V² = k/m (A² - x²)
V = √(K/m (A² - x²) )
note x = ½A
V = √(k/m (A² - (½A)²)
V = √(k/m (A² - A²/4))
Resolve the fraction between A.
V = √(¾. K/m. A² )
V = √(¾ * (18.4/0.0359)*(0.395)²)
V = √(0.75 * 512.53 * 0.156)
V = √(59.966)
V = 7.74m/s
Answer:
e) 120m/s
Explanation:
When the ball reaches its highest point, its velocity becomes zero, meaning
.
where 
is the initial velocity.
Solving for 
we get
which is the time it takes the ball to reach the highest point.
Now, after the ball has reached its highest point, it turns around and falls downwards. After time 
since it had reached the highest point, the ball has traveled downwards and the velocity 
it has gained is
,
and we are told that this is twice the initial velocity ; therefore,
which gives
Thus, the total time taken to reach velocity 
is
This 
, we are told, is 36 seconds; therefore,
and solving for we get:
which from the options given is choice e.
