word problems - speed and velocity

Question

1. A truck’s speed increases uniformly from 36 kph to 108 kph. In 20 seconds. Determine the following:

1. Average speed (velocity)
2. The acceleration in meter/sec.
3. The distance in meter covered during this period.

Answer 1

The initial velocity is V_o = (36 km/hr)( 1000m/km)(hr/3600 s) = 10 m/s

The final velocity is V_f = (108 km/hr)(1000m/km)(hr/3600s)= 30 m/s

The average velocity is V_ave = (V_o+V_f)/2 =(30 m/s + 10 m/s) / 2 = 20 m/s

The acceleration is given by the following formula V_f = at + V_o , at = (V_f - V_o) / t , a = (30 m/s - 10 m/s)/ 20s

a = 1 m/s²

The distance is given by either of the following formulas

V_f² - V_o² = 2.a.X , X = V_f² - V_o² / 2a = [(30m/s)² - (10m/s)²] / 2( 1m/s²) = 800 m²/s² / 2 m/s² = 400 m

or X = 1/2 a t² + V_ot + X₀, where X₀ = 0 starting from the point where the velocity was initially 10 m/s

X = 1/2 ( 1m/s²)(20s)² + ( 10m/s)(20s) = 1/2(400 m) + (200 m) = 200 m+200m = 400 m