Hello.

An object is observed to move along the x-axis with a varying velocity; v(x)=C[x(d−x)]^1/2, where C=9.0/s and d=48.0m

A. Use computer simulation to calculate the time it will take for the object to travel from x=0 to x=d.

Hint: Subdivide the x-axis into N parts of width Δx=d/N. The time for the object to move from xn to xn+1 is Δt=Δx/v(x_a); here x_a=0.5(x_n + x_n+1). Now add up all the time intervals.

B. Calculate the max speed during this time (plot the function)

c = 9.0;

d = 48.0;

n = 10;

v[x_] := c (x (d - x))^(1/2)

r = Range[0, d, d/n]

p = Partition[r, 2, 1]

xa = Mean /@ p

deltaV = v /@ xa

deltaT = (d/n)/deltaV

Total[deltaT]

Plot[v[x], {x, 0, d}]

FindMaximum[v[x], x]

Here's a code from Mathematica program

Top speed is = 216 at x = 24

But how to find time it will take for x to travel from 0 to 48?