Answer:
A.) 39.5 m
B.) 0
C.) 60m/s^2
Explanation:
Given that a displacement function of a particle is x(t)=(20t^2-15t+200).
To Find the total displacement,
Reduce everything by dividing them by 5
X(t) = 4t^2 - 3t + 40 ...... (1)
For instantaneous velocity, differentiate x(t). That is,
dy/dt = 60t - 15 ...... (2)
But dy/dt = velocity.
If dy/dt = 0, then
60t - 15 = 0
60t = 15
t = 15/60
t = 0.25s
Substitutes t in equation (1)
Total displacement will be
X(t) = 4(0.25)^2 - 3(0.25) + 40
X(t) = 0.25 - 0.75 + 40
Total displacement = 39.5 m
To calculate instantaneous velocity, substitute t into equation (2)
V = 60 (0.25) - 15
V = 0.
and to find instantaneous acceleration, differentiate dv/dt
dv/dt = 60
Therefore, acceleration = 60 m/s^2
<h2>
Answer:</h2>
(a) 3.96 x 10⁵C
(b) 4.752 x 10⁶ J
<h2>
Explanation:</h2>
(a) The given charge (Q) is 110 A·h (ampere hour)
Converting this to A·s (ampere second) gives the number of coulombs the charge represents. This is done as follows;
=> Q = 110A·h
=> Q = 110 x 1A x 1h [1 hour = 3600 seconds]
=> Q = 110 x A x 3600s
=> Q = 396000A·s
=> Q = 3.96 x 10⁵A·s = 3.96 x 10⁵C
Therefore, the number of coulombs of charge is 3.96 x 10⁵C
(b) The energy (E) involved in the process is given by;
E = Q x V -----------------(i)
Where;
Q = magnitude of the charge = 3.96 x 10⁵C
V = electric potential = 12V
Substitute these values into equation (i) as follows;
E = 3.96 x 10⁵ x 12
E = 47.52 x 10⁵ J
E = 4.752 x 10⁶ J
Therefore, the amount of energy involved is 4.752 x 10⁶ J
Answer:
20 ms¯¹
Explanation:
3. Determination of the final velocity
From the question given above, the following data were obtained:
Time (t) = 4 s
Acceleration (a) = 5 ms¯²
Initial velocity (u) = 0 ms¯¹
Final velocity (v) =?
Acceleration is simply defined as the change in velocity per unit time.
Mathematically, it can be expressed as:
Acceleration (a) = final velocity – Initial velocity / time
a = v – u / t
With the above formula, we can obtain the final velocity of the car as follow:
Time (t) = 4 s
Acceleration (a) = 5 ms¯²
Initial velocity (u) = 0 ms¯¹
Final velocity (v) =?
a = v – u / t
5 = v – 0 / 4
5 = v / 4
Cross multiply
v = 5 × 4
v = 20 ms¯¹
Thus, the final velocity of the car is 20 ms¯¹
