Answer:
B. 14.4 N
Rotational speed (Angular Velocity) = 2
The Radius of the circle = 1.2 m
Velocity = Angular velocity × radius = 2×1.2 = 2.4 m/s
Centripetal force= mv²/r = 3 × 2.4×2.4/1.2 = 3 × 2.4 × 2
= 14.4 N
Answer: a) 7.71 m/s², b) - 6.67 m/s²
Explanation: first thing to note is that
1 mile = 1609.34
1 hour = 3600s
Hence, 100mph to m/s = (100 × 1609.34)/3600 = 44.71 m/s
Initial velocity (u) = 0, final velocity (v) = 44.71 m/s, t = 5.8s, a = acceleration =?
By using newton's laws of motion
v = u + at
44.71 = 0 + a(5.8)
44.71 = 5.8a
a = 44.71/5.8
a = 7.71 m/s²
Question b)
The car is completing a stop which implies that the car is coming to rest, and when a car is coming to rest, the final velocity (v) is zero.
Hence u = 34 m/s, v = 0, a =?, t = 5.1 s
v = u + at
0 = 34 + a(5.1)
a(5.1) = - 34
a = - 34/5.1
a = - 6.67 m/s².
The negative sign beside the acceleration shows that the body is decelerating
Apply this kinematics equation for the particle's vertical motion:
D = Vt + 0.5At²
D = vertical distance traveled, t = time, V = initial vertical velocity, A = vertical acceleration
Given values:
D = 49m
V = 34.3m/s
A = -9.81m/s²
Plug in and solve for t:
49 = 34.3t - 4.905t²
4.905t² - 34.3t + 49 = 0
Use the quadratic roots formula to find the values of t:
t ≈ 2, 5
The particle reaches a height of 49m at t = 2s & t = 5s
Answer:
The product of the two numbers is 2.33* 10^13
Explanation:
Given
4.31x10⁷ and 5.41x10⁵
Required
Multiply
The multiplication of the two digits is represented as thus:
This can also be rewritten as
Multiply 4.31 and 5.41
Apply laws of indices
The scientific notation is always in the form:
Where
So:
23.3171 can be rewritten as 2.33171 * 10
So, we have:
Also, apply law of indices again
It's always advisable (but not compulsory to approximate to 1 or 2 decimal places)
So:
<em>Hence; the product of the two numbers is 2.33* 10^13</em>