A bus traveling at +30 km/hr accelerates at a constant +3.5 m/s2 for 6.8 s. What is its final velocity in km/hr?
3.5 m/s^2 * 1km/1000m * (1hr/3600s)^2 = 12.6 km/hr/s
so, v = 30km/hr + 12.6km/hr/s * 6.8s= 30.238 115.68 km/hr
or, since 30 km/hr = 8.33 m/s,
8.33 + 3.5*6.8 = 33.13 m/s = 115.668 km/hr
Vo = 30km/h = 30,000m/3600s = 8.33 m/s.
V = Vo + a*T = 8.33 + 3.5*6.8 = 32.1 m/s.
V = 32.1m/s = 0.0321*3600 = 115.7 km/h.
Well, to calculate the final velocity in km/hr, we can start by converting the acceleration from m/s² to km/hr². But let's be honest, who even uses km/hr² in everyday life? So instead, I'll tell you a joke.
Why don't scientists trust atoms?
Because they make up everything!
Now, back to the question. To convert the acceleration from m/s² to km/hr², we need to multiply it by a conversion factor. Since there are 1000 meters in a kilometer and 3600 seconds in an hour, the conversion factor is (1000/3600) km/hr². After converting the acceleration, you can multiply it by the time of 6.8 seconds to get the change in velocity.
But wait, there's more! We need to take into account the initial velocity of the bus, which is given as +30 km/hr. So we add the change in velocity to the initial velocity to find the final velocity.
However, let's not forget another joke before we continue.
What do you get when you cross a snowman and a vampire?
Frostbite!
Alright, back to business. With the change in velocity and the initial velocity, we can finally calculate the final velocity. Just remember that in math, speed and velocity are different. Speed is just how fast something is going, while velocity includes the direction.
So, after doing the math and considering all the jokes, the final velocity of the bus will be... *drumroll*
To solve this problem, we need to use the formula relating acceleration, initial velocity, final velocity, and time:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given information:
u = +30 km/hr (initial velocity)
a = +3.5 m/s^2 (acceleration)
t = 6.8 s (time)
To solve the problem, we need to convert the initial velocity from km/hr to m/s.
1 km = 1000 m
1 hr = 3600 s
So, to convert km/hr to m/s, we can multiply it by (1000 m / 3600 s):
u = 30 km/hr * (1000 m / 3600 s)
Simplifying:
u = 8.33 m/s (initial velocity)
Now, we can use the formula:
v = u + at
v = 8.33 m/s + (3.5 m/s² * 6.8 s)
v = 8.33 m/s + 23.8 m/s
v = 32.13 m/s (final velocity)
Finally, we need to convert the final velocity from m/s to km/hr.
v = 32.13 m/s * (3600 s / 1000 m)
v = 115.67 km/hr
Therefore, the final velocity of the bus is +115.67 km/hr.
To find the final velocity of the bus in km/hr, we need to follow these steps:
Step 1: Convert the initial velocity from km/hr to m/s.
Given that the bus is traveling at +30 km/hr, we need to convert it to m/s. To do this, we will use the conversion factor 1 km/hr = 0.2778 m/s.
Initial velocity in m/s = 30 km/hr * 0.2778 m/s = 8.334 m/s
Step 2: Calculate the acceleration.
Given that the bus accelerates at a constant +3.5 m/s², we don't need to make any conversions.
Acceleration = 3.5 m/s²
Step 3: Calculate the final velocity.
To calculate the final velocity, we will use the formula:
Final velocity = Initial velocity + (Acceleration * Time)
Given:
Initial velocity = 8.334 m/s
Acceleration = 3.5 m/s²
Time = 6.8 s
Final velocity = 8.334 m/s + (3.5 m/s² * 6.8 s) = 8.334 m/s + 23.8 m/s = 32.134 m/s
Step 4: Convert the final velocity from m/s to km/hr.
To convert the final velocity from m/s to km/hr, we will use the conversion factor 1 m/s = 3.6 km/hr.
Final velocity in km/hr = 32.134 m/s * 3.6 km/hr = 115.6824 km/hr
Therefore, the final velocity of the bus is approximately 115.68 km/hr.