An object moves such that acceleration a(t)=2(1-3t). Given v(0)=-5 and x(0)=4, find x(1).
1 answer:
Answer:
x(1) = -1
Step-by-step explanation:
Given the equation for acceleration of the object as;
a(t)=2(1-3t)
a(t) = 2-6t
Integrate to get the velocity
v(t) = 2t-6t²/2 + C
v(t) = 2t-3t²+C
If v(0) = -5
when t = 0 v = -5
-5 = 2(0)-3(0)²+C
-5 = C
C = -5
v(t) = 2t-3t²-5
To get the displacement x(t), we will integrate the velocity function
x(t) = 2t²/2-3t³/3-5t+C
x(t) = t²-t³-5t+C
If x(0) = 4
At t = 0, x(t) = 4
4 = 0²-0³-5(0)+C
4 = C
C = 4
x(t) = t²-t³-5t+4
Get x(1)
x(1) = 1²-1³-5(1)+4
x(1) = 1-1-5+4
x(1) = -5+4
x(1) = -1
Hence x(1) = -1
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