Question

4. The velocity in mm/s of an object moving on a straight line is 200 multiplied by s (s given in mm). If the starting point at time zero is s time required to reach this position 0.5m, what is its acceleration when s 2m and the

The velocity in mm/s of an object moving on a straight line is 200 multiplied by s (s given in mm). If the starting point at time zero is s = 0.5m, what is its acceleration when s = 2m and the time required to reach this position.

Answer 1

v = 200 s a = dv/dt = dv/ds ds/dt = dv/ds v = v dv/ds = v d/ds (200 s) = 200 v = 20 times (200 times s) = (200)^2 times 2000 mm/s^2 = 8 times 10^7 mm/s^2 = 8 times 10^4 m/s^2 v = ds/dt = 200s rightdoublearrow integral ds/s = 200 integral dt ln s_2/s_1 = 200t t = 1/200 ln(2/0.5) = 0.00693 s rightdoublearrow t = 0.00693 s