Amotor cycle is moving up an incline of 1 in 30 at a speed of 80 km/h, and then suddenly the engine shuts down. the tractive resistance of the motor is 5% of its weight. if no external force is applied and applying the law of conservation of energy, determine.
(i) the maximum distance it will travel before coming to rest
(ii)time the motor cycle will take to come to rest
(iii) deceleration of the motor cycle

(i) 24.4 m

(ii) 2.19 s

(iii) -10.1 m/s²

Explanation:

(i) Kinetic energy = potential energy + work

KE = PE + W

½ mv² = mgh + Fd

We know the resistance force is 5% of the weight, so F = 0.05mg.

We know the slope of the incline is 1/30, so h = d/√(1²+30²).

½ mv² = mgd/√(1²+30²) + mgd

½ mv² = mgd (1/√901 + 1)

d = v² / (2g (1/√901 + 1))

Given v = 80 km/h = 22.2 m/s:

d = 24.4 m

(ii) Given:

Δx = 24.4 m

v₀ = 22.2 m/s

v = 0 m/s

Find: t

Δx = ½ (v + v₀) t

(24.4 m) = ½ (0 m/s + 22.2 m/s) t

t = 2.19 s

(iii) Given:

Δx = 24.4 m

v₀ = 22.2 m/s

v = 0 m/s

Find: a

v² = v₀² + 2aΔx

(0 m/s)² = (22.2 m/s)² + 2a (24.4 m)

a = -10.1 m/s²

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