2 An indoor track is 100 meters in diameter A runner increas

2. An indoor track is 100 meters in diameter. A runner increases his speed at a constant rate from 4 m/s to 8 m/s over a distance of 30 meters. Determine the total acceleration of the runner 3 seconds after he begins to increase his speed. 3. A boat travels in a circular path of radius 400 ft. Its speed varies as a function of time according to v = 6(t-t). Determine

Solution

Initial velocity (u) = 4 m/s

Final velocity (v) = 8 m/s

Distance travelled (s) = 30 m

Let tangential acceleration be a m/s².

v² - u² = 2as

=> 8² - 4² = 2 x a x 30

=> a = 0.8 m/s²

Velocity (v_f) after 3 seconds = u + a t = 4 + 0.8 x 3 = 6.4 m/s

Diameter of track = 100 m

Radius of track (r) = 50 m

Centripetal acceleration (a_c) = v_f² / r = 6.4² / 50 = 0.8192 m/s²

Total acceleration = ( a² + a_c² )^0.5 = ( 0.8² + 0.8192² )^0.5 = 1.145 m/s²