A particle travels along x-axis. its position at time t is function x(t) = (t+1)^(1/2) . What is ratio of average speed of particle over interval 0 ≤ t ≤ 3 to instantaneous speed of particle at t = 3?

Question

A) 1/4

B) 3/4

C) 4/3

D) 4/1

Answer 1

x(t) = (t+1)^1/2

The average speed over the interval [0,3] is the slope of the line connecting the endpoints of x(t) on the interval:

average speed = ((x(3)-x(0)) / (3-0) = ____?

The instantaneous speed is the derivative of x(t) wrt t:

Instantaneous speed = dx(t)/dt = _____?

Now evaluate dx(t)/dt at x = 3 and take the ratio to get the answer:

(average speed) / (dx(3)/dt) = ____?