Question

You are in a car (car A) traveling at a constant speed of 72 mph (miles per hour) when another car (car B) 25 meters ahead of your swerves into your lane. Car B is traveling at 100 km/hr. In order to avoid colliding with car B, determine the minimum acceleration of your car (A).

a) For both cars, sketch acceleration- and velocity-versus-time graphs. (Be sure to label them.) When sketching a graph, you should show the rough behavior (i.e., approximately linear, parabolic, etc.)

b) Evaluate the answer that you found in part a) by using 'limiting case' analysis. In other words, consider what would happen if one of the variables in your expression from part A becomes very large or very small. At this extreme value, is the behavior of the acceleration expected and/or reasonable? If not, this may indicate that something is wrong with your expression.

Answer 1

Va= 72 miles/hr= 32.19 m/s

Vb= 100 km/hr= 27.78 m/s

Vba= Vb - Va= 32.19-27.78= 4.41 m/s. (Relative velocity of A w.r.t B)

Sba= 25 m

V^2 - U^2= 2aS

0 - Vba^2= 2a×Sba

Hence a= - Vba^2/2Sba= -4.41^2/2×25= -0.389 m/s^2.

The above acceleration is actually the relative acceleration of B w.r.t A. But the acceleration of B is itself 0....hence acceleration of A is -0.389 m/s^2.

a)

b) we know that a= - Vba^2/2Sba

If Vba becomes very large(which means Va>>>>Vb) then the magnitude of the acceleration tends to infinity while if Sba becomes very parge (which means distance between them is very large ) then a tends to 0.

But a will always be -ve.