The motorist, under uniform acceleration, travels 10,875 units in the 10th second based on simultaneous equations derived from the 3rd and 8th-second distance data.
To solve this problem, we need to use the equations of motion for uniformly accelerating motion:
Given that the motorist is uniformly accelerating, we can find the acceleration 'a' using the information provided.
Let's use the information that in the 3rd second, the motorist travels 15 minutes:
t = 3 seconds, d = 15 minutes.
Convert minutes to seconds: 15 minutes = 15 * 60 seconds = 900 seconds.
Now, use the equation d = ut + (1/2)at^2 to find the acceleration:
900 = u(3) + (1/2)a(3)^2
Similarly, for the information that in the 8th second, the motorist travels 25 minutes:
t = 8 seconds, d = 25 minutes.
Convert minutes to seconds: 25 minutes = 25 * 60 seconds = 1500 seconds.
Use the equation d = ut + (1/2)at^2:
1500 = u(8) + (1/2)a(8)^2
Now, you have two equations with two unknowns (u and a). Solve these equations simultaneously to find u and a.
Once you have u and a, you can use the same equations to find the distance traveled in the 10th second (t = 10 seconds).
To find the final answer, solve the system of equations:
Equation 1: 900 = u(3) + (1/2)a(3)^2
Equation 2: 1500 = u(8) + (1/2)a(8)^2
Now, simplify the equations:
Equation 1: 900 = 3u + (9/2)a
Equation 2: 1500 = 8u + 16a
Now, you have a system of two equations with two unknowns:
3u + (9/2)a = 900
8u + 16a = 1500
To solve this system, use the substitution method:
From Equation 1, solve for u:
3u + (9/2)a = 900
3u = 900 - (9/2)a
u = 300 - (3/2)a
Now substitute this expression for u into Equation 2:
8u + 16a = 1500
8(300 - (3/2)a) + 16a = 1500
2400 - 12a + 16a = 1500
4a = 900
a = 225
Now that you have the value for a, substitute it back into the expression for u:
u = 300 - (3/2)a
u = 300 - (3/2)(225)
u = 300 - 675/2
u = -37.5
Now that you have u and a, you can find the distance traveled in the 10th second (t = 10 seconds) using the equation d = ut + (1/2)at^2:
d = (-37.5)(10) + (1/2)(225)(10)^2
d = -375 + (1/2)(225)(100)
d = -375 + 11250
d = 10875
Therefore, the motorist will travel 10875 units of distance in the 10th second.