A motorcycle is travelling at a constant acceleration in a straight line. When it passes by the first lamp post, it is travelling at 10ms-1. When is passes by the next lamp post which is 200m from the first lamp post, the motor cycle is travelling at 16 ms-1. What is the acceleration of the motorcycle.
Options:
A: 0.17 ms-2
B: 0.22 ms-2
C: 0.39 ms-2
D: 0.89 ms-2
What i did:
Let distance from starting point to first lamp post be x
Time taken for motorcycle to reach first lamp post would be (10/x)
Time taken to reach second lamp post would be (16/200+x)
Through a velocity time graph, acceleration would equal to rise/run which is equal to (6/((200+x/10)-(x/10)) which by solving i get acceleration = (960/2000-6x).
I still have an unknown. Help?
V^2 = Vo^2 + 2a*d = 16^2
10^2 + 2a*200 = 256
400a = 256-100 = 156
a = 0.39 m/s^2.
To find the acceleration of the motorcycle, you need to eliminate the unknown variable (x) by setting up a system of equations with the given information and solving for x.
Let's set up the equations using the information provided:
Equation 1: When the motorcycle passes the first lamp post, it is traveling at 10 m/s. This suggests that the motorcycle has traveled distance x:
x = 10t₁, where t₁ is the time taken to reach the first lamp post.
Equation 2: When the motorcycle passes the second lamp post, which is 200m from the first lamp post, it is traveling at 16 m/s. This suggests that the motorcycle has traveled distance (x + 200):
x + 200 = 16t₂, where t₂ is the time taken to reach the second lamp post.
Now, we can solve this system of equations to find x:
From Equation 1, we can express t₁ in terms of x: t₁ = x/10.
Substitute this expression for t₁ into Equation 2:
x + 200 = 16(x/10)
x + 200 = (16/10)x
10(x + 200) = 16x
10x + 2000 = 16x
2000 = 16x - 10x
2000 = 6x
x = 2000/6
x = 333.33 m (rounded to two decimal places)
Now that we have found x, we can substitute it back into either Equation 1 or Equation 2 to find the time taken:
Using Equation 1:
t₁ = x/10
t₁ = 333.33/10
t₁ = 33.33 s (rounded to two decimal places)
Now that we have the time, we can calculate the acceleration using the formula:
acceleration = (change in velocity) / (time taken)
The change in velocity is 16 m/s - 10 m/s = 6 m/s.
acceleration = 6 m/s / 33.33 s
acceleration ≈ 0.18 m/s² (rounded to two decimal places)
Comparing this value to the options provided, it seems that none of the options match exactly. However, the closest option is A: 0.17 m/s².