A train starts from rest and accelerates uniformly, until it has traveled 2.1 km

Question

A train starts from rest and accelerates uniformly, until it has traveled 2.1 km and acquired a velocity of 24 m/s. The train then moves at a constant velocity of 24 m/s for 10 minutes. The train then slows down uniformly at 0.0065 m/s^2, until it is brought to a halt. What is the total distance traveled by the train? A motorist makes a trip of 180 miles. For the first 90 miles, she drives at a constant speed of 30 mph. At what constant speed must she drive the remaining distance if her average speed for the total trip is to be 40 mph? The magnitude of A vector is 5.5 units. Vector A vector lies in the second quadrant and forms an angle of 34 degrees with the y-axis. What is the components, A_x and A_y of this vector? You walk 55 m to the north, then turn 60 degree to your right and walk another 45 m. How far are you from where you originally started?

Explanation / Answer

here,

1)

for accelrating period ,

the distance travelled , d1 = 2.1 km

for constant speed phase

distance travelled , d2 = v * t

d2 = 24 * 10 * 60 = 14400 m = 14.4 km

for deaccelrating period

the distance travelled , d3 = v^2 /(2a)

d3 = 24^2 /( 2 * 0.0065)

d3 = 44307 m = 44.3 km

the total distance travelled , d =d1 + d2 + d3

d = 60.8 km

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