Question

1. a particle starts at x = 0 and moves along the x - axis with velocity v(t)=5 for time t≥0. where is the particle at t = 4?

Explanation:

Step1: Recall the relationship between velocity and position

The position function $x(t)$ is the antiderivative of the velocity function $v(t)$. Since $v(t)=5$, then $x(t)=\int v(t)dt=\int 5dt = 5t + C$.

Step2: Determine the constant of integration

The particle starts at $x = 0$ when $t = 0$. Substitute $x(0)=0$ into $x(t)=5t + C$. We get $0=5\times0 + C$, so $C = 0$. Thus, $x(t)=5t$.

Step3: Find the position at $t = 4$

Substitute $t = 4$ into $x(t)=5t$. Then $x(4)=5\times4=20$.

Answer:

20