79. A commuter train can minimize the time t between two stations by accelerating (a, = 0.1 m/s2) for a time
tį then undergoing a negative acceleration (az =
-0.5 m/s2) by using his brakes for a time ty. Since the
stations are only 1 km apart, the train never reaches its
maximum velocity. Find the minimum time of travelt,
and the time t.

Let the train remains under acceleration for time t₁ and under deceleration for time t₂ .

The final velocity under acceleration becomes the initial velocity of deceleration.

.1 t₁ = .5 t₂

t₁ = 5 t₂

Now , total distance travelled is 1000 m

1/2 a₁t₁² + 1/2 a₂ t₂² = 1000

a₁t₁² + a₂ t₂² = 2000

.1 x 25 t₂² + .5 t₂² = 2000

3 t₂² = 2000

t₂² = 666.67

t₂ = 25.82 s

t₁ = 25.82 x 5 = 129.1 s

Total time = 154.92 s

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