Question

At 2:00 p.m. a car's speedometer reads 30 mi/h. At 2:30 p.m. it reads 50 mi/h. Show that at some time between 2:00 and 2:30 the acceleration is exactly 40 mi/h2.

Answer 1

The acceleration is exactly 40 mi/h² as shown

Step-by-step explanation:

Given;

initial velocity of the car, u = 30 mi/h

final velocity of the car, v = 50 mi/h

change in velocity, ΔV = v - u

ΔV = 50 mi/h - 30 mi/h = 20 mi/h

initial time, t₁ = 2:00 PM

final time, t₂ = 2:30 PM

Change in time, Δt = t₂ - t₁

Δt = 2: 30 - 2:00 = 30 mins = 0.5 hour

Acceleration is given as change in velocity per change in time;

a = ΔV / Δt

`a = (20 \ mi/h)/(0.5 \ h)\\\\a = 40 \ mi/h^2 \ (shown)\\\\`

Therefore, the acceleration is exactly 40 mi/h² as shown.