On a one-lane road, a person driving a car at V₁ = 57 mph suddenly notices a truck 1.1 mi in front of him. That person is moving in the same direction at V₂ = 45 mi/h. In order to avoid a collision, the person has to reduce the speed of his car to V₂ during the time interval Δt. The smallest magnitude of acceleration required for the car to avoid a collision is a. During this problem, assume the direction of motion of the car is the positive direction.
(a) Write an expression, in terms of defined quantities, for the distance ΔX₂ traveled by the truck during the time interval Δt.
(b) Enter the expression for the distance ΔX₁ traveled by the car in terms of V₁, V₂, and a.
(c) Enter an expression for the acceleration of the car, a, in terms of V₁, V₂, and Δt.
(d) Enter an expression for ΔX₁ in terms of ΔX₂ and d when the driver just barely avoids collision.
(e) Enter an expression for ΔX₁ in terms of V₁, V₂, and Δt.
(f) Enter an expression for Δt in terms of D, V₁, and V₂.
(g) Calculate the value of Δt in hours.
(h) Use the expressions you entered in part (c) and (f) and enter an expression for a in terms of d, V₁, and V₂.
(i) Calculate the value of a in meters per second.