Question

Two vehicles A and B are being observed as they travel along a simulated expressway. Below are the spatio-temporal and rate properties of each vehicle:

Vehicle A:

•Position from point of origin= 60.96 m

•Speed= 40.225 kph

•Acceleration= 1.609 kph per second

Vehicle B:

•Position from point of origin= 0m

•Speed= 96.54kph

•Acceleration= 0kph per second

Simulationtime= 400 seconds

Determine:

a. What is the difference in distance between vehicles A and B at 50% of simulation time?

b.What is the instant speed of vehicle A at t=350 seconds?

Answer 1

there are two vehicles A and B, vehicle A has an acceleration, increase in velocity with time and vehicle B has no acceleration, velocity is constant throughout the simulation time.

(a) At 50% of simulation time, t = (0.5) * 400 = 200 seconds

Vehicle A:

initial velocity(t = 0), u = ? final velocity(at t = 200 s), v = 40.225 kph = 11.173 m/s (1 kph = 5/18 m/s)

v = u + a*t acceleration, a = 1.609 kph/s = 0.447 m/s2

11.174 = u + (0.447)*(200)

u = -78.226 m/s

position, s = u*t + (0.5) a*t2

at t = 200s, S = (-78.226)*(200) + (0.5)*(0.447)*(200)2 = - 6705.2 m

Vehicle B :

s = u*t + 0 ( acceleration = 0)

u = 96.54 kph = 26.82 m/s

s = 26.82 * 200 = 5363.33 m

difference between positions = SB - SA = 5363.33 - (-6705.2) = 12068.53 m

= 12.068 km

(b)speed of vehicle A (at time t = 350 s)

v = u + a*t (values given in (a))

v = -78.226 + (0.447)*(350)

v = 78.224 m/s (+ve) = 281.606 kph