A train accelarates uniformly in a straight line at 0.3m/s^2 from rest. Calculate the velocity 15 seconds after its departure. Calculate time taken to reach 30km/h and calculate Distance covered by the train
(a)
v=at=0.3•15=0.45 m/s
(b)
v₁=30km/h=30000/3600 =833.3 m/s
t₁=v₁/a=833.3/0.3 =2777.8 s.
(c)
s=v₁²/2a= 833.3²/2•0.3=1157314 m =1157 km
To calculate the velocity of the train 15 seconds after its departure, we can use the formula:
v = u + at,
where:
v = final velocity,
u = initial velocity (in this case, rest),
a = acceleration,
t = time.
Given:
u = 0 m/s (since the train is at rest),
a = 0.3 m/s^2,
t = 15 s,
we can substitute these values into the formula to find v:
v = 0 + (0.3 * 15) = 4.5 m/s.
Therefore, the velocity of the train 15 seconds after its departure is 4.5 m/s.
To calculate the time taken to reach 30 km/h (m/s), we need to convert the given speed from km/h to m/s:
30 km/h = (30 * 1000) / (60 * 60) = 8.33 m/s.
Using the same formula as above, v = u + at, we can rearrange it to solve for t:
t = (v - u) / a.
Given:
u = 0 m/s (since the train is at rest),
a = 0.3 m/s^2,
v = 8.33 m/s,
we can substitute these values into the formula:
t = (8.33 - 0) / 0.3 = 27.77 s.
Therefore, the time taken to reach 30 km/h is approximately 27.77 seconds.
To calculate the distance covered by the train, we can use the equation:
s = ut + (1/2)at^2,
where:
s = distance,
u = initial velocity,
a = acceleration,
t = time.
Given:
u = 0 m/s (since the train is at rest),
a = 0.3 m/s^2,
t = 15 s,
we can substitute these values into the formula to find s:
s = (0 * 15) + (1/2) * 0.3 * (15^2) = 33.75 m.
Therefore, the distance covered by the train is 33.75 meters.