Question

a particle starts at x=0 and moves along the x-axis with velocity v(t) =5 for time t greater than or less than 0. where is the particle at t=4

Answer 1

Answer:

at t=4, the particle is at x = 20

Step-by-step explanation:

This question revolves around velocity and displacement of a particle moving in a straight line (along the x-axis). At t = 0 the particle is at x = 0. The velocity of the particle as function of time is given as;

v(t) = 5

The velocity is thus constant, implying further that the particle has 0 acceleration.

To find the position of the particle at t = 4, we employ integral calculus since displacement is an integral of velocity while velocity is a derivative of displacement.

In short, we shall be integrating the velocity function between t =0 and t = 4 to find its location at t = 4.

$\int\limits^4_0 {5} \, dt$

The integral of 5 with respect to t is 5t + c but we ignore the constant of integration since we are dealing with a definite integral;

5t

The final step is to substitute t with the limits given;

5(4) - 5(0) = 20

The particle was moving along the x-axis, so its new position would be;

x = 20